This book addresses the confinement problem, which concerns the behavior of non-abelian gauge theories, and the force which is mediated by gauge fields, at large distances. The word “confinement” in the context of hadronic physics originally referred to the fact that quarks and gluons appear to be trapped inside mesons and baryons, from which they cannot escape. There are other, and possibly deeper meanings that can be attached to the term, and these will be explored in this book. Although the confinement problem is far from solved, much is now known about the general features of the confining force, and there are a number of very well motivated theories of confinement which are under active investigation. This volume gives a both pedagogical and concise introduction and overview of the main ideas in this field, their attractive features, and, as appropriate, their shortcomings. This second edition summarizes some of the developments in this area which have occurred since the first edition of this book appeared in 2011. These include new results in the caloron/dyon picture of confinement, in functional approaches, and in studies of the Yang-Mills vacuum wave functional.  Special attention, in two new chapters, is given to recent numerical investigations of the center vortex theory, and to the varieties of confinement which may exist in gauge-Higgs theories.Reviews of the first edition:“This is indeed a very good book. I enjoyed reading it and… I learned a lot from it.… It is definitely a research book that provides readers with a guide to the most updated confinement models.” (Giuseppe Nardelli, Mathematical Reviews, Issue 2012 d)“The book is beautifully produced with special emphasis on the relevance of center symmetry and lattice formulation as well as an introduction to current research on confinement.” (Paninjukunnath Achuthan, Zentralblatt MATH, Vol. 1217, 2011)

The idea of synthesizing quantum electrodynamics (QED) and the kinetic theory of plasmas ?rst occurred to me in the early 1970s [1, 2]. The project to do so has been carried out bit by bit over the subsequent years. The name “quantum plasmadynamics” (QPD) is my own jargon [3] for the synthesized theory. Both QED and the kinetic theory of plasmas areconcerned with the int- action between charged particles and the electromagnetic ?eld, but they are radically di?erent in the way the interaction is described. The kinetic theory of plasmas is a collective-medium theory: a plasma is not a collection of - dependent particles in a given electromagnetic ?eld, but a medium in which the particles collectively modify the ?eld, and the ?eld modi?es the par- cles. The charge and current densities associated with the particles are part of a self-consistent ?eld. Conventionally, the kinetic theory of plasmas is a classical theory: the motions of particles are treated using classical dynamics.

This book is based on material taught in general and special theoretical physics courses given by I.B. Khriplovich at the Physics Department of Novosibirsk University, Russia. The book contains the analysis of concrete problems in classical mechanics, classical electrodynamics, quantum mechanics, and relativistic quantum mechanics. To the best of Khriplovich's knowledge, many of the problems and solutions included in this book have never been discussed in print before.

The reviews presented in this volume cover a huge range of cluster of galaxies topics. Readers will find the book essential reading on subjects such as the physics of the ICM gas, the internal cluster dynamics, and the detection of clusters using different observational techniques. The expert chapter authors also cover the huge advances being made in analytical or numerical modeling of clusters, weak and strong lensing effects, and the large scale structure as traced by clusters.

Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics.The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations.This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.1)     Published under theauspices of the Royal Astronomical Society.

The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.

The idea of synthesizing quantum electrodynamics (QED) and the kinetic theory of plasmas ?rst occurred to me in the early 1970s [1, 2]. The project to do so has been carried out bit by bit over the subsequent years. The name “quantum plasmadynamics” (QPD) is my own jargon [3] for the synthesized theory. Both QED and the kinetic theory of plasmas areconcerned with the int- action between charged particles and the electromagnetic ?eld, but they are radically di?erent in the way the interaction is described. The kinetic theory of plasmas is a collective-medium theory: a plasma is not a collection of - dependent particles in a given electromagnetic ?eld, but a medium in which the particles collectively modify the ?eld, and the ?eld modi?es the par- cles. The charge and current densities associated with the particles are part of a self-consistent ?eld. Conventionally, the kinetic theory of plasmas is a classical theory: the motions of particles are treated using classical dynamics.

Whydowelookatsomethingsandthinktheyarebeautifulwhileotherthingsdo notappearestheticallypleasingtous?Thisisaquestionthathasalwaysinterested mankind. Oneanswerisgivenbythefollowingquotationfromanearlypresidentof theCollegeofNewJersey(nowPrincetonUniversity): "Beautyisfoundinimmaterialthingslikeproportionoruniformity...calledbyvariousnamesofregularity,order,uniformity,symmetry, 1 proportion,harmony,etc. "...JonathanEdwards Symmetrynotonlyprovidesthenaturalharmonythatmakessomethingappear beautifultous,butalsoisofgreatvaluetosciencebecauseitdictatesthephysical traitsofmanyobjects. Natureitselfseemstolovebeautysinceatomstendtoself? assemble into shapes with speci?c symmetry and crystals grow in geometric lattices. Inmanycases,ifweknowthesymmetryofsomethingwecanpredict someofitsimportantpropertieswithouthavingtoresorttoexperimentationor complicatedcalculations. One area where the concept of symmetry plays an important role is that of crystalline solids. Crystals, by their very nature, exhibit speci?c symmetries. Crystallinematerialshavemanyimportantapplicationsindevicesbasedontheir electronic,optical,thermal,magnetic,andmechanicalproperties.Solidstatep- sicistsandchemists,aswellasmaterialscientistsandengineers,havedeveloped rigorousquantumtheoreticalmodelstodescribethesepropertiesandsophisticated measurementtechniquestoverifythesemodels. Manytimes,however,inscreeningmaterialsforanewapplicationitisuseful to be able to quickly and easily determine if a speci?c material will have the appropriatepropertieswithoutmakingdetailedcalculationsorexperiments. This canbedonebyanalyzingthesymmetrypropertiesofthematerial. Themathema- calformalismthathasbeendevelopedtoaccomplishthisiscalledgrouptheory. Thesymmetrypropertiesofacrystalcanbedescribedbyagroupofmathematical 1 J. Edwards,WorksofJonathanEdwards(BannerofTruthTrust,Edinburgh,1979) v vi Preface operations. Thenusingsimplegrouptheoryprocedures,thephysicalpropertiesof thecrystalcanbedetermined. Duringthe45yearsIhavebeeninvolvedinteachingandresearchinvarious areasofsolidstatephysics,Ihavemadeextensiveuseoftheconceptsofgroup theory. YetIhavebeensurprisedathowlittleemphasisthistopicreceivesinany formaleducationalcurriculum.Generally,astudentstudyingsolidstatephysicsor chemistrywillbeexposedtocrystalstructuresearlyinthesemesterandthenhave nofurtherexposuretocrystalsymmetryuntilsomespecialtopicsuchasnonlinear opticsisdiscussed. Thisbookfocusesonthesymmetryofcrystalsandthedescr- tionofthissymmetrythroughtheuseofgrouptheory. Althoughspeci?cexamples are provided of using this formalism to determine both the microscopic and macroscopicpropertiesofmaterials,theemphasisisonthecomprehensive,per- sivenatureofsymmetryinallareasofsolidstatescience. Theintentofthebookistobeareferencesourceforthosedoingresearchor teachinginsolidstatescienceandengineering,oratextforaspecialtycoursein grouptheoryappliedtothepropertiesofcrystals. Tucson,AZ RichardC. Powell June2010 Contents 1 SymmetryinSolids...1 1. 1 Symmetry...1 1. 2 CrystalStructures...4 1. 3 SymmetryinReciprocalSpace...15 1. 4 Problems...24 References...24 2 GroupTheory...25 2. 1 BasicConceptsofGroupTheory...27 2. 2 CharacterTables...31 2. 3 GroupTheoryExamples...40 2. 3. 1 C PointGroup...40 3v 2. 3. 2 O PointGroup...45 h 2. 4 GroupTheoryinQuantumMechanics...47 2. 5 Problems...52 References...53 3 TensorPropertiesofCrystals...55 3. 1 First-RankMatterTensors...57 3. 2 Second-RankMatterTensors...62 3. 3 Third-RankMatterTensors...68 3. 4 Fourth-RankMatterTensors...73 3. 5 Problems...77 References...77 4 SymmetryPropertiesofPointDefectsinSolids...79 4. 1 EnergyLevelsofFreeIons...79 4. 2 CrystalFieldSymmetry...85 4. 3 EnergyLevelsofIonsinCrystals...87 vii viii Contents 4. 4 Example:d?Electrons...95 4. 5 Example:f-Electrons...100 4. 6 Problems...104 References...104 5 SymmetryandtheOpticalPropertiesofCrystals ...

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.

Quantum Plasmadynamics is a synthesis of the kinetic theory of plasmas and quantum electrodynamics (QED). In this volume, the approach applied to unmagnetized plasmas in volume 1 is generalized to magnetized plasmas. First, a covariant version of nonquantum kinetic theory is formulated for single-particle (emission and scattering)  processes and the collective-medium response. The relativistic quantum treatment is based on solutions of Dirac's equation for an electron in a magnetostatic field, and single-particle processes are treated using a magnetized version of QED. The response of an electron gas is derived by generalizing the derivation of the response of the magnetized vacuum.

“Transport Processes in Space Physics and Astrophysics”  is aimed at graduate level students to provide the necessary mathematical and physics background to understand the transport of gases, charged particle gases, energetic charged particles, turbulence, and radiation in  an astrophysical and space physics context. Subjects emphasized in the work include collisional and collisionless processes in gases (neutral or plasma), analogous processes in turbulence fields and radiation fields, and allows for a simplified treatment of the statistical description of the system. A systematic study that addresses the common tools at a graduate level allows students to progress to a point where they can begin their research in a variety of fields within space physics and astrophysics. This book is for graduate students who expect to complete their research in an area of plasma space physics or plasma astrophysics. By providing a broad synthesis in several areas of transport theory and modeling, the work also benefits researchers in related fields by providing an overview that currently does not exist. For numerous interesting and challenging space physics and astrophysics problems, there is a need to describe the “long-term” behavior of systems governed by macroscopic laws and microscopic randomness. A random event has an outcome that is uncertain and unpredictable, yet the collective behavior of a system can be governed by well defined mathematical and physical principles. Examples of physical problems include the behavior of gases in the presence of microscopic inter-particle collisions, the evolution of a gas of charged protons and electrons (a plasma), the collective propagation of solar energetic particles or cosmic rays in a magnetically turbulent medium, the collective behavior of dust in an accretion disk subject to coagulation and destruction, the evolution of low-frequency magnetic field turbulence in the inhomogeneous solar wind, or the transport of photosin a partially ionized interstellar medium. This book provides graduate students with a unified introduction to the physics of collective phenomena or transport processes for gases (charged and uncharged), fields, and photons in a space physics or astrophysics context.

Lasers can readily remove very thin layers from small areasof a material and can thus be used both to control thestructure of the surface and to determine its composition.Laser ablation thus has a wide variety of applications -from re-shaping the cornea of the eye to correct vision andmicro-machining electronic devices, to detection of minutecontaminants on catalysts. This book is the proceedings ofone ofthe first workshops held on this topic.

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are:Surface charges as conserved quantities in theories of gravity;Classical and holographic features of three-dimensional Einstein gravity;Asymptotically flat spacetimes in four dimensions: BMS group and memory effects;The Kerr black hole: properties at extremality and quasi-normal mode ringing.Each topic starts with historical foundations and points to a few modern research directions.

This book introduces a quantum-mechanical description of the nuclear fission process from an initial compound state to scission. Issues like the relevant degrees of freedom throughout the process, the way of coupling collective and intrinsic degrees during the fission process, and how a nucleus divides into two separate daughters in a quantum-mechanical description where its wave function can be non-local, are currently being investigated through a variety of theoretical, computational, and experimental techniques.The term “microscopic” in this context refers to an approach that starts from protons, neutrons, and an effective (i.e., in-medium) interaction between them. The form of this interaction is inspired by more fundamental theories of nuclear matter, but still contains parameters that have to be adjusted to data. Thus, this microscopic approach is far from complete, but sufficient progress has been made to warrant taking stock of what has been accomplished so far.Theaim is to provide, in a pedagogical and comprehensive manner, one specific approach to the fission problem, originally developed at the CEA Bruyères-le-Châtel Laboratory in France.Intended as a reference for advanced graduate students and researchers in fission theory as well as for practitioners in the field, it includes illustrative examples throughout the text to make it easier for the reader to understand, implement, and verify the formalism presented.

This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Most of the matter in our universe is in a gaseous or plasma state. Yet, most textbooks on quantum statistics focus on examples from and applications in condensed matter systems, due to the prevalence of solids and liquids in our day-to-day lives. In an attempt to remedy that oversight, this book consciously focuses on teaching the subject matter in the context of (dilute) gases and plasmas, while aiming primarily at graduate students and young researchers in the field of quantum gases and plasmas for some of the more advanced topics. The majority of the material is based on a two-semester course held jointly by the authors over many years, and has benefited from extensive feedback provided by countless students and co-workers. The book also includes many historical remarks on the roots of quantum statistics: firstly because students appreciate and are strongly motivated by looking back at the history of a given field of research, and secondly because the spirit permeating this book has been deeply influenced by meetings and discussions with several pioneers of quantum statistics over the past few decades.

This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.

This concise primer reviews the latest developments in the field of jets. Jets are collinear sprays of hadrons produced in very high-energy collisions, e.g. at the LHC or at a future hadron collider. They are essential to and ubiquitous in experimental analyses, making their study crucial.At present LHC energies and beyond, massive particles around the electroweak scale are frequently produced with transverse momenta that are much larger than their mass, i.e., boosted. The decay products of such boosted massive objects tend to occupy only a relatively small and confined area of the detector and are observed as a single jet. Jets hence arise from many different sources and it is important to be able to distinguish the rare events with boosted resonances from the large backgrounds originating from Quantum Chromodynamics (QCD). This requires familiarity with the internal properties of jets, such as their different radiation patterns, a field broadly known as jet substructure.This set of notes begins by providing a phenomenological motivation, explaining why the study of jets and their substructure is of particular importance for the current and future program of the LHC, followed by a brief but insightful introduction to QCD and to hadron-collider phenomenology. The next section introduces jets as complex objects constructed from a sequential recombination algorithm. In this context some experimental aspects are also reviewed. Since jet substructure calculations are multi-scale problems that call for all-order treatments (resummations), the bases of such calculations are discussed for simple jet quantities.With these QCD and jet physics ingredients in hand, readers can then dig into jet substructure itself. Accordingly, these notes first highlight the main concepts behind substructure techniques and introduce a list of the main jet substructure tools that have been used over the past decade. Analytic calculations are then provided for several families of tools, the goal being to identify their key characteristics. In closing, the book provides an overview of LHC searches and measurements where jet substructure techniques are used, reviews the main take-home messages, and outlines future perspectives.

Dark matter is a frequently discussed topic in contemporary particle physics. Written strictly in the language of particle physics and quantum field theory, these course-based lecture notes focus on a set of standard calculations that students need in order to understand weakly interacting dark matter candidates. After introducing some general features of these dark matter agents and their main competitors, the Higgs portal scalar and supersymmetric neutralinos are introduced as our default models. In turn, this serves as a basis for exploring four experimental aspects: the dark matter relic density extracted from the cosmic microwave background; indirect detection including the Fermi galactic center excess; direct detection; and collider searches. Alternative approaches, like an effective theory of dark matter and simplified models, naturally follow from the discussions of these four experimental directions.

Colloidal plasmas - a still emerging field of plasma physics - enable the study of basic plasma properties on a microscopic kinetic level and allow the visualization of collective plasma phenomena, like oscillations and waves. Moreover, a vast number of novel phenomena are found in these systems, ranging from Coulomb crystallization to new types of forces and waves. Last but not least, they shed a new light on various traditional aspects of plasma physics such as shielding or the mechanism of acoustic waves in plasmas, thus providing new insight into the basic foundations of plasma physics.These course-based and self-contained lecture notes provide a general introduction to this active and growing field to students and nonspecialists, requiring only basic prior knowledge in plasma physics. ​

This book is based on Valery Zagrebaev's original papers and lecture materials on nuclear physics with heavy ions, which he prepared and extended through many years for the students of nuclear physics specialties.Thе book outlines the main experimental facts on nuclear reactions involving heavy ions at low energies. It focuses on discussions of nuclear physics processes that are a subject of active, modern research and it gives illustrative explanations of these phenomena in the framework of up-to-date theoretical concepts.This textbook is intended for students in physics who have completed a standard course of quantum mechanics and have basic ideas of nuclear physics processes.It is designed as a kind of lifeboat that, at the end of the course, will allow students to navigate the modern scientific literature and to understand the goals and objectives of current, on-going research.

This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds.This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.

This book provides an introduction to topics in non-equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation, of Kolmogorov type, which is needed to describe an isolated atom (actually, in experiments, an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmann's classical (non-quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions, particularly because, if the temperature is low enough, such a gas is known to have at equilibrium a transition, the Bose–Einstein transition, where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough.

Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are notwell discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

This concise book introduces and discusses the basic theory of conical intersections with applications in atomic, molecular and condensed matter physics.Conical intersections are linked to the energy of quantum systems. They can occur in any physical system characterized by both slow and fast degrees of freedom - such as e.g. the fast electrons and slow nuclei of a vibrating and rotating molecule - and are important when studying the evolution of quantum systems controlled by classical parameters. Furthermore, they play a relevant role for understanding the topological properties of condensed matter systems.Conical intersections are associated with many interesting features, such as a breakdown of the Born-Oppenheimer approximation and the appearance of nontrivial artificial gauge structures, similar to the Aharonov-Bohm effect.Some applications presented in this book include- Molecular Systems: some molecules in nonlinear nuclear configurations undergo Jahn-Teller distortions under which the molecule lower their symmetry if the electronic states belong to a degenerate irreducible representation of the molecular point group.- Solid State Physics: different types of Berry phases associated with conical intersections can be used to detect topologically nontrivial states of matter, such as topological insulators, Weyl semi-metals, as well as Majorana fermions in superconductors.- Cold Atoms: the motion of cold atoms in slowly varying inhomogeneous laser fields is governed by artificial gauge fields that arise when averaging over the fast internal degrees of freedom of the atoms. These gauge fields can be Abelian or non-Abelian, which opens up the possibility to create analogs to various relativistic effects at low speed.

Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume.  To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.

Fundamentals of Magnonics is a textbook for beginning graduate students in the areas of magnetism and spintronics. The level of presentation assumes only basic knowledge of the origin of magnetism and electromagnetism, and quantum mechanics. The book utilizes elementary mathematical derivations, aimed mainly at explaining the physical concepts involved in the phenomena studied and enabling a deeper understanding of the experiments presented. Key topics include the basic phenomena of ferromagnetic resonance in bulk materials and thin films, semi-classical theory of spin waves, quantum theory of spin waves and magnons, magnons in antiferromagnets, parametric excitation of magnons, nonlinear and chaotic phenomena, Bose-Einstein condensation of magnons, and magnon spintronics. Featuring end-of-chapter problem sets accompanied by extensive contemporary and historical references, this book provides the essential tools for any graduate or advanced undergraduate-level course of studieson the emerging field of magnonics.

This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.

This book addresses the confinement problem, which concerns the behavior of non-abelian gauge theories, and the force which is mediated by gauge fields, at large distances. The word “confinement” in the context of hadronic physics originally referred to the fact that quarks and gluons appear to be trapped inside mesons and baryons, from which they cannot escape. There are other, and possibly deeper meanings that can be attached to the term, and these will be explored in this book. Although the confinement problem is far from solved, much is now known about the general features of the confining force, and there are a number of very well motivated theories of confinement which are under active investigation. This volume gives a both pedagogical and concise introduction and overview of the main ideas in this field, their attractive features, and, as appropriate, their shortcomings. This second edition summarizes some of the developments in this area which have occurred since the first edition of this book appeared in 2011. These include new results in the caloron/dyon picture of confinement, in functional approaches, and in studies of the Yang-Mills vacuum wave functional.  Special attention, in two new chapters, is given to recent numerical investigations of the center vortex theory, and to the varieties of confinement which may exist in gauge-Higgs theories.Reviews of the first edition:“This is indeed a very good book. I enjoyed reading it and… I learned a lot from it.… It is definitely a research book that provides readers with a guide to the most updated confinement models.” (Giuseppe Nardelli, Mathematical Reviews, Issue 2012 d)“The book is beautifully produced with special emphasis on the relevance of center symmetry and lattice formulation as well as an introduction to current research on confinement.” (Paninjukunnath Achuthan, Zentralblatt MATH, Vol. 1217, 2011)

The idea of synthesizing quantum electrodynamics (QED) and the kinetic theory of plasmas ?rst occurred to me in the early 1970s [1, 2]. The project to do so has been carried out bit by bit over the subsequent years. The name “quantum plasmadynamics” (QPD) is my own jargon [3] for the synthesized theory. Both QED and the kinetic theory of plasmas areconcerned with the int- action between charged particles and the electromagnetic ?eld, but they are radically di?erent in the way the interaction is described. The kinetic theory of plasmas is a collective-medium theory: a plasma is not a collection of - dependent particles in a given electromagnetic ?eld, but a medium in which the particles collectively modify the ?eld, and the ?eld modi?es the par- cles. The charge and current densities associated with the particles are part of a self-consistent ?eld. Conventionally, the kinetic theory of plasmas is a classical theory: the motions of particles are treated using classical dynamics.

This book is based on material taught in general and special theoretical physics courses given by I.B. Khriplovich at the Physics Department of Novosibirsk University, Russia. The book contains the analysis of concrete problems in classical mechanics, classical electrodynamics, quantum mechanics, and relativistic quantum mechanics. To the best of Khriplovich's knowledge, many of the problems and solutions included in this book have never been discussed in print before.

The reviews presented in this volume cover a huge range of cluster of galaxies topics. Readers will find the book essential reading on subjects such as the physics of the ICM gas, the internal cluster dynamics, and the detection of clusters using different observational techniques. The expert chapter authors also cover the huge advances being made in analytical or numerical modeling of clusters, weak and strong lensing effects, and the large scale structure as traced by clusters.

Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics.The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations.This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.1)     Published under theauspices of the Royal Astronomical Society.

The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.

The idea of synthesizing quantum electrodynamics (QED) and the kinetic theory of plasmas ?rst occurred to me in the early 1970s [1, 2]. The project to do so has been carried out bit by bit over the subsequent years. The name “quantum plasmadynamics” (QPD) is my own jargon [3] for the synthesized theory. Both QED and the kinetic theory of plasmas areconcerned with the int- action between charged particles and the electromagnetic ?eld, but they are radically di?erent in the way the interaction is described. The kinetic theory of plasmas is a collective-medium theory: a plasma is not a collection of - dependent particles in a given electromagnetic ?eld, but a medium in which the particles collectively modify the ?eld, and the ?eld modi?es the par- cles. The charge and current densities associated with the particles are part of a self-consistent ?eld. Conventionally, the kinetic theory of plasmas is a classical theory: the motions of particles are treated using classical dynamics.

Whydowelookatsomethingsandthinktheyarebeautifulwhileotherthingsdo notappearestheticallypleasingtous?Thisisaquestionthathasalwaysinterested mankind. Oneanswerisgivenbythefollowingquotationfromanearlypresidentof theCollegeofNewJersey(nowPrincetonUniversity): "Beautyisfoundinimmaterialthingslikeproportionoruniformity...calledbyvariousnamesofregularity,order,uniformity,symmetry, 1 proportion,harmony,etc. "...JonathanEdwards Symmetrynotonlyprovidesthenaturalharmonythatmakessomethingappear beautifultous,butalsoisofgreatvaluetosciencebecauseitdictatesthephysical traitsofmanyobjects. Natureitselfseemstolovebeautysinceatomstendtoself? assemble into shapes with speci?c symmetry and crystals grow in geometric lattices. Inmanycases,ifweknowthesymmetryofsomethingwecanpredict someofitsimportantpropertieswithouthavingtoresorttoexperimentationor complicatedcalculations. One area where the concept of symmetry plays an important role is that of crystalline solids. Crystals, by their very nature, exhibit speci?c symmetries. Crystallinematerialshavemanyimportantapplicationsindevicesbasedontheir electronic,optical,thermal,magnetic,andmechanicalproperties.Solidstatep- sicistsandchemists,aswellasmaterialscientistsandengineers,havedeveloped rigorousquantumtheoreticalmodelstodescribethesepropertiesandsophisticated measurementtechniquestoverifythesemodels. Manytimes,however,inscreeningmaterialsforanewapplicationitisuseful to be able to quickly and easily determine if a speci?c material will have the appropriatepropertieswithoutmakingdetailedcalculationsorexperiments. This canbedonebyanalyzingthesymmetrypropertiesofthematerial. Themathema- calformalismthathasbeendevelopedtoaccomplishthisiscalledgrouptheory. Thesymmetrypropertiesofacrystalcanbedescribedbyagroupofmathematical 1 J. Edwards,WorksofJonathanEdwards(BannerofTruthTrust,Edinburgh,1979) v vi Preface operations. Thenusingsimplegrouptheoryprocedures,thephysicalpropertiesof thecrystalcanbedetermined. Duringthe45yearsIhavebeeninvolvedinteachingandresearchinvarious areasofsolidstatephysics,Ihavemadeextensiveuseoftheconceptsofgroup theory. YetIhavebeensurprisedathowlittleemphasisthistopicreceivesinany formaleducationalcurriculum.Generally,astudentstudyingsolidstatephysicsor chemistrywillbeexposedtocrystalstructuresearlyinthesemesterandthenhave nofurtherexposuretocrystalsymmetryuntilsomespecialtopicsuchasnonlinear opticsisdiscussed. Thisbookfocusesonthesymmetryofcrystalsandthedescr- tionofthissymmetrythroughtheuseofgrouptheory. Althoughspeci?cexamples are provided of using this formalism to determine both the microscopic and macroscopicpropertiesofmaterials,theemphasisisonthecomprehensive,per- sivenatureofsymmetryinallareasofsolidstatescience. Theintentofthebookistobeareferencesourceforthosedoingresearchor teachinginsolidstatescienceandengineering,oratextforaspecialtycoursein grouptheoryappliedtothepropertiesofcrystals. Tucson,AZ RichardC. Powell June2010 Contents 1 SymmetryinSolids...1 1. 1 Symmetry...1 1. 2 CrystalStructures...4 1. 3 SymmetryinReciprocalSpace...15 1. 4 Problems...24 References...24 2 GroupTheory...25 2. 1 BasicConceptsofGroupTheory...27 2. 2 CharacterTables...31 2. 3 GroupTheoryExamples...40 2. 3. 1 C PointGroup...40 3v 2. 3. 2 O PointGroup...45 h 2. 4 GroupTheoryinQuantumMechanics...47 2. 5 Problems...52 References...53 3 TensorPropertiesofCrystals...55 3. 1 First-RankMatterTensors...57 3. 2 Second-RankMatterTensors...62 3. 3 Third-RankMatterTensors...68 3. 4 Fourth-RankMatterTensors...73 3. 5 Problems...77 References...77 4 SymmetryPropertiesofPointDefectsinSolids...79 4. 1 EnergyLevelsofFreeIons...79 4. 2 CrystalFieldSymmetry...85 4. 3 EnergyLevelsofIonsinCrystals...87 vii viii Contents 4. 4 Example:d?Electrons...95 4. 5 Example:f-Electrons...100 4. 6 Problems...104 References...104 5 SymmetryandtheOpticalPropertiesofCrystals ...

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.

Quantum Plasmadynamics is a synthesis of the kinetic theory of plasmas and quantum electrodynamics (QED). In this volume, the approach applied to unmagnetized plasmas in volume 1 is generalized to magnetized plasmas. First, a covariant version of nonquantum kinetic theory is formulated for single-particle (emission and scattering)  processes and the collective-medium response. The relativistic quantum treatment is based on solutions of Dirac's equation for an electron in a magnetostatic field, and single-particle processes are treated using a magnetized version of QED. The response of an electron gas is derived by generalizing the derivation of the response of the magnetized vacuum.

“Transport Processes in Space Physics and Astrophysics”  is aimed at graduate level students to provide the necessary mathematical and physics background to understand the transport of gases, charged particle gases, energetic charged particles, turbulence, and radiation in  an astrophysical and space physics context. Subjects emphasized in the work include collisional and collisionless processes in gases (neutral or plasma), analogous processes in turbulence fields and radiation fields, and allows for a simplified treatment of the statistical description of the system. A systematic study that addresses the common tools at a graduate level allows students to progress to a point where they can begin their research in a variety of fields within space physics and astrophysics. This book is for graduate students who expect to complete their research in an area of plasma space physics or plasma astrophysics. By providing a broad synthesis in several areas of transport theory and modeling, the work also benefits researchers in related fields by providing an overview that currently does not exist. For numerous interesting and challenging space physics and astrophysics problems, there is a need to describe the “long-term” behavior of systems governed by macroscopic laws and microscopic randomness. A random event has an outcome that is uncertain and unpredictable, yet the collective behavior of a system can be governed by well defined mathematical and physical principles. Examples of physical problems include the behavior of gases in the presence of microscopic inter-particle collisions, the evolution of a gas of charged protons and electrons (a plasma), the collective propagation of solar energetic particles or cosmic rays in a magnetically turbulent medium, the collective behavior of dust in an accretion disk subject to coagulation and destruction, the evolution of low-frequency magnetic field turbulence in the inhomogeneous solar wind, or the transport of photosin a partially ionized interstellar medium. This book provides graduate students with a unified introduction to the physics of collective phenomena or transport processes for gases (charged and uncharged), fields, and photons in a space physics or astrophysics context.

Lasers can readily remove very thin layers from small areasof a material and can thus be used both to control thestructure of the surface and to determine its composition.Laser ablation thus has a wide variety of applications -from re-shaping the cornea of the eye to correct vision andmicro-machining electronic devices, to detection of minutecontaminants on catalysts. This book is the proceedings ofone ofthe first workshops held on this topic.

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are:Surface charges as conserved quantities in theories of gravity;Classical and holographic features of three-dimensional Einstein gravity;Asymptotically flat spacetimes in four dimensions: BMS group and memory effects;The Kerr black hole: properties at extremality and quasi-normal mode ringing.Each topic starts with historical foundations and points to a few modern research directions.

This book introduces a quantum-mechanical description of the nuclear fission process from an initial compound state to scission. Issues like the relevant degrees of freedom throughout the process, the way of coupling collective and intrinsic degrees during the fission process, and how a nucleus divides into two separate daughters in a quantum-mechanical description where its wave function can be non-local, are currently being investigated through a variety of theoretical, computational, and experimental techniques.The term “microscopic” in this context refers to an approach that starts from protons, neutrons, and an effective (i.e., in-medium) interaction between them. The form of this interaction is inspired by more fundamental theories of nuclear matter, but still contains parameters that have to be adjusted to data. Thus, this microscopic approach is far from complete, but sufficient progress has been made to warrant taking stock of what has been accomplished so far.Theaim is to provide, in a pedagogical and comprehensive manner, one specific approach to the fission problem, originally developed at the CEA Bruyères-le-Châtel Laboratory in France.Intended as a reference for advanced graduate students and researchers in fission theory as well as for practitioners in the field, it includes illustrative examples throughout the text to make it easier for the reader to understand, implement, and verify the formalism presented.

This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Most of the matter in our universe is in a gaseous or plasma state. Yet, most textbooks on quantum statistics focus on examples from and applications in condensed matter systems, due to the prevalence of solids and liquids in our day-to-day lives. In an attempt to remedy that oversight, this book consciously focuses on teaching the subject matter in the context of (dilute) gases and plasmas, while aiming primarily at graduate students and young researchers in the field of quantum gases and plasmas for some of the more advanced topics. The majority of the material is based on a two-semester course held jointly by the authors over many years, and has benefited from extensive feedback provided by countless students and co-workers. The book also includes many historical remarks on the roots of quantum statistics: firstly because students appreciate and are strongly motivated by looking back at the history of a given field of research, and secondly because the spirit permeating this book has been deeply influenced by meetings and discussions with several pioneers of quantum statistics over the past few decades.

This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.

This concise primer reviews the latest developments in the field of jets. Jets are collinear sprays of hadrons produced in very high-energy collisions, e.g. at the LHC or at a future hadron collider. They are essential to and ubiquitous in experimental analyses, making their study crucial.At present LHC energies and beyond, massive particles around the electroweak scale are frequently produced with transverse momenta that are much larger than their mass, i.e., boosted. The decay products of such boosted massive objects tend to occupy only a relatively small and confined area of the detector and are observed as a single jet. Jets hence arise from many different sources and it is important to be able to distinguish the rare events with boosted resonances from the large backgrounds originating from Quantum Chromodynamics (QCD). This requires familiarity with the internal properties of jets, such as their different radiation patterns, a field broadly known as jet substructure.This set of notes begins by providing a phenomenological motivation, explaining why the study of jets and their substructure is of particular importance for the current and future program of the LHC, followed by a brief but insightful introduction to QCD and to hadron-collider phenomenology. The next section introduces jets as complex objects constructed from a sequential recombination algorithm. In this context some experimental aspects are also reviewed. Since jet substructure calculations are multi-scale problems that call for all-order treatments (resummations), the bases of such calculations are discussed for simple jet quantities.With these QCD and jet physics ingredients in hand, readers can then dig into jet substructure itself. Accordingly, these notes first highlight the main concepts behind substructure techniques and introduce a list of the main jet substructure tools that have been used over the past decade. Analytic calculations are then provided for several families of tools, the goal being to identify their key characteristics. In closing, the book provides an overview of LHC searches and measurements where jet substructure techniques are used, reviews the main take-home messages, and outlines future perspectives.

Dark matter is a frequently discussed topic in contemporary particle physics. Written strictly in the language of particle physics and quantum field theory, these course-based lecture notes focus on a set of standard calculations that students need in order to understand weakly interacting dark matter candidates. After introducing some general features of these dark matter agents and their main competitors, the Higgs portal scalar and supersymmetric neutralinos are introduced as our default models. In turn, this serves as a basis for exploring four experimental aspects: the dark matter relic density extracted from the cosmic microwave background; indirect detection including the Fermi galactic center excess; direct detection; and collider searches. Alternative approaches, like an effective theory of dark matter and simplified models, naturally follow from the discussions of these four experimental directions.

Colloidal plasmas - a still emerging field of plasma physics - enable the study of basic plasma properties on a microscopic kinetic level and allow the visualization of collective plasma phenomena, like oscillations and waves. Moreover, a vast number of novel phenomena are found in these systems, ranging from Coulomb crystallization to new types of forces and waves. Last but not least, they shed a new light on various traditional aspects of plasma physics such as shielding or the mechanism of acoustic waves in plasmas, thus providing new insight into the basic foundations of plasma physics.These course-based and self-contained lecture notes provide a general introduction to this active and growing field to students and nonspecialists, requiring only basic prior knowledge in plasma physics. ​

This book is based on Valery Zagrebaev's original papers and lecture materials on nuclear physics with heavy ions, which he prepared and extended through many years for the students of nuclear physics specialties.Thе book outlines the main experimental facts on nuclear reactions involving heavy ions at low energies. It focuses on discussions of nuclear physics processes that are a subject of active, modern research and it gives illustrative explanations of these phenomena in the framework of up-to-date theoretical concepts.This textbook is intended for students in physics who have completed a standard course of quantum mechanics and have basic ideas of nuclear physics processes.It is designed as a kind of lifeboat that, at the end of the course, will allow students to navigate the modern scientific literature and to understand the goals and objectives of current, on-going research.

This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds.This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.

This book provides an introduction to topics in non-equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation, of Kolmogorov type, which is needed to describe an isolated atom (actually, in experiments, an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmann's classical (non-quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions, particularly because, if the temperature is low enough, such a gas is known to have at equilibrium a transition, the Bose–Einstein transition, where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough.

Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are notwell discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

This concise book introduces and discusses the basic theory of conical intersections with applications in atomic, molecular and condensed matter physics.Conical intersections are linked to the energy of quantum systems. They can occur in any physical system characterized by both slow and fast degrees of freedom - such as e.g. the fast electrons and slow nuclei of a vibrating and rotating molecule - and are important when studying the evolution of quantum systems controlled by classical parameters. Furthermore, they play a relevant role for understanding the topological properties of condensed matter systems.Conical intersections are associated with many interesting features, such as a breakdown of the Born-Oppenheimer approximation and the appearance of nontrivial artificial gauge structures, similar to the Aharonov-Bohm effect.Some applications presented in this book include- Molecular Systems: some molecules in nonlinear nuclear configurations undergo Jahn-Teller distortions under which the molecule lower their symmetry if the electronic states belong to a degenerate irreducible representation of the molecular point group.- Solid State Physics: different types of Berry phases associated with conical intersections can be used to detect topologically nontrivial states of matter, such as topological insulators, Weyl semi-metals, as well as Majorana fermions in superconductors.- Cold Atoms: the motion of cold atoms in slowly varying inhomogeneous laser fields is governed by artificial gauge fields that arise when averaging over the fast internal degrees of freedom of the atoms. These gauge fields can be Abelian or non-Abelian, which opens up the possibility to create analogs to various relativistic effects at low speed.

Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume.  To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.

Fundamentals of Magnonics is a textbook for beginning graduate students in the areas of magnetism and spintronics. The level of presentation assumes only basic knowledge of the origin of magnetism and electromagnetism, and quantum mechanics. The book utilizes elementary mathematical derivations, aimed mainly at explaining the physical concepts involved in the phenomena studied and enabling a deeper understanding of the experiments presented. Key topics include the basic phenomena of ferromagnetic resonance in bulk materials and thin films, semi-classical theory of spin waves, quantum theory of spin waves and magnons, magnons in antiferromagnets, parametric excitation of magnons, nonlinear and chaotic phenomena, Bose-Einstein condensation of magnons, and magnon spintronics. Featuring end-of-chapter problem sets accompanied by extensive contemporary and historical references, this book provides the essential tools for any graduate or advanced undergraduate-level course of studieson the emerging field of magnonics.

This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.