Classical Dynamics of Linear and Nonlinear Systems

Gyaneshwar P. Srivastava is Emeritus Professor of Theoretical Condensed Matter Physics at Exeter University, UK. In a teaching career of over 45 years he has taught several physics modules, including analytical and chaotic dynamics. His research has concentrated on theoretical and computational studies of the physics of phonons and electrons in crystalline solids, surfaces and nano-structures. He has collaborated with various physicists, both experimentalists and theorists, of international reputation. This has led to over 500 publications, including several review articles and three postgraduate books. He is an Outstanding Referee for APS journals.

This is a welcome revision, about 30 years after the first edition, of one of the most comprehensive monographs on the theory of phonons. The author has made considerable contributions to research in many of the areas he describes. As well as introducting new topics, the updated edition covers new methods or improved techniques for the calculations covered in the first edition.The groundwork is established in the first two chapters, covering the elements of crystal symmetry and the reciprocal lattice and the simeclassical treatment of lattice dynamics moving from one to three dimensions, considering simples models of interatomic forces, and discussing lattice specific heat. This is followed by three comprehensive chapters on the ab initio calculation of phonos in the harmonic approximation, including both direct and linear response methods, anharmonicity, and lattice thermal conductivity, including relaxation-time, variational and linear response methods. Chapter 6 discusses the mechanism of phonon scattering from imperfections, through anharmonic processes (including their ab initio treatment), and from interactions with electrons and magnetic impurities in semiconductors. The following chapter brings all of this together in the context of thermal conductivity, again progressing from simple phenomenological approaches to the latest quantitatively reliable calculations. The methods are illustrated with applications to a variety of bulk materials.The remaining seven chapters cover more specialised aspects of phonons. Some of these are for special geometries, such as surfaces, for special structures, such as layered cyrstal and nanocomposites, or for disordered materials such as impure and mixed crystal and quasi-crystalline and amorphous solids. The remaining topics are topological nanophononics and chiral phononics, phonon spectroscopy, and phonons in liquid helium.The approach throughout is theoretical and rigorous. The extensive references include work up to 2021, and updated appendices bring the material on ab initio calculations up to date. The index has been completely revised for this edition, and in some parts is less helpful than that of the first edition. Although the revision is only 13 pages longer than the original, the larger page format and reduced size of figures have allowed a lot more material to be included. This is an excellent monograph, worthy of a place on the shelf of anybody working on phonons.- A.H. Harker, Physics and Astronomy, UCL (reitred).

• SECTION I General considerationsChapter 1 Classification of Dynamics and Scope of This BookSECTION II Linear dynamics of particles and objectsChapter 2 Dynamics of Particles and Objects in Configuration SpaceChapter 3 Dynamics of Particles and Objects in Phase SpaceSECTION III Linear dynamics of interacting particlesChapter 4 Dynamics of Linear Molecules and Linear Atomic ChainsChapter 5 Dynamics of Two- and Three-Dimensional CrystalsSECTION IV Nonlinear dynamicsChapter 6 Non-linear Motion and Chaos – TheoryChapter 7 Non-linear Motion and Chaos – ApplicationsSECTION V Elements of classical field theoryChapter 8 Lagrangian and Hamiltonian of a Classical FieldSECTION VI Beyond classical mechanicsChapter 9 Elements of Quantum Field TheoryChapter 10 Classical and Quantum Perturbation TheoriesAppendix A Mathematical PreliminariesAppendix B Conservative Property of Central ForcesAppendix C Euler-Lagrange Variational PrincipleAppendix D Introduction to Matrix EigensolutionsAppendix E Reciprocal Lattice and Brillouin ZoneAppendix F Numerical Solution of Differential EquationsAppendix G Analytic Solution of Second Order Linear Inhomogeneous DifferentialEquationsAnswers to Selected ProblemsReferencesIndex