Introduction to Green's Function Methods in Many-Body Physics

With Applications to Quantum Transport

Inbunden, Engelska, 2026

1 203 kr

Kommande

Beskrivning

This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics. It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit. The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara function methods. The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches. Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters. The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers. More than 200 problems have been included to support learning, with selected solutions available at the end of each chapter. Instructors benefit from access to the full solutions manual.

Produktinformation

Utgivningsdatum:2026-10-31
Format:Inbunden
Språk:Engelska
Antal sidor:800
Förlag:Cambridge University Press
ISBN:9781009790147

Utforska kategorier

Mer om författaren

Lev Kantorovich is a theoretical condensed matter physicist and has been a professor at King's College London since 2009. He is author of 'Quantum Theory of the Solid State' and the two-volume 'Mathematics for Natural Scientists,' now in its second edition. He is a recipient of the 2023 David Tabor Medal and Prize.

Innehållsförteckning

List of Abbreviations; Part I. Preliminaries: 1. Second quantisation ignoring spin; 2. Second quantisation via relativistic treatment of many electrons; 3. Operators, interactions, Hamiltonians, mean field and linear response; Part II. Equilibrium: 4. Single-particle two-time Green's functions; 5. Matsubara (imaginary time) Green's functions; 6. Feynman diagrams for Matsubara Green's Functions; Part III. Non-Equilibrium: 7. Green's functions for non-equilibrium: definition and main properties; 8. Feynman diagrams for NEGF: perturbation theory; 9. Feynman diagrams for NEGF: variational approach; Part IV. Quantum Transport Applications: 10. Quantum transport in molecular junctions: steady state; 11. Quantum transport in molecular junctions: time-dependent bias; 12. Localised spins and transport: Kondo problem; A. Non-Hermitian Hamiltonian; B. Angular momentum of an electron; C. Canonical transformation; D. The delta function; References; Index.