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E-raamat: Annotations to Quantum Statistical Mechanics [Taylor & Francis e-raamat]

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  • Formaat: 274 pages, 2 Line drawings, black and white; 2 Illustrations, black and white
  • Ilmumisaeg: 20-Mar-2018
  • Kirjastus: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9781315196596
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Annotations to Quantum Statistical MechanicsSuurem pilt
  • Formaat: 274 pages, 2 Line drawings, black and white; 2 Illustrations, black and white
  • Ilmumisaeg: 20-Mar-2018
  • Kirjastus: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9781315196596
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781315196596
This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Bayms lectures that were presented in the book Quantum Statistical Mechanics: Greens Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Greens functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Greens functions with sufficient and rigorous details.

In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He started the tedious work of rewriting and annotating them to fully understand the formalism of nonequilibrium quantum statistical mechanics. While doing so, he realized they can be a useful resource for students of modern physics but will have to be upgraded to match pace with the evolved curricula. Being aware that besides completing the course work and passing the relevant examinations, it is necessary for graduate students of modern physics to make the knowledge of a topic concrete in their minds. This book is a systematically prepared summary of those lectures and will be extremely useful for graduate students as well as senior researchers to settle down the key knowledge of the subject.
Preface xi
Preface of Quantum Statistical Mechanics: Green's Function Methods in Equilibrium and Nonequilibrium Problems xv
1 Physical Prerequisites
1(32)
1.1 Basic Quantum Mechanics
1(11)
1.2 Representations and Equations of Motion
12(11)
1.3 Second Quantization
23(10)
2 Mathematical Introduction
33(10)
2.1 Basic Definitions
33(4)
2.2 The Boundary Condition
37(6)
3 Information Contained in G>: and G<
43(8)
3.1 Dynamical Information
43(3)
3.2 Statistical Mechanical Information Contained in G
46(5)
4 The Hartree and Hartree--Fock Approximations
51(12)
4.1 Equations of Motion
51(3)
4.2 Free Particles
54(1)
4.3 Hartree Approximation
55(5)
4.4 Hartree-Fock Approximation
60(3)
5 Effects of Collisions on G
63(14)
5.1 Lifetime of Single-Particle States
63(2)
5.2 Born Approximation Collisions
65(4)
5.3 Structure of σc and A
69(3)
5.4 Interpretation of the Born Collision Approximation
72(3)
5.5 Boltzmann Equation Interpretation
75(2)
6 A Technique for Deriving Green's Function Approximations
77(12)
6.1 Ordinary Perturbation Theory
81(4)
6.2 Expansion of σ in V and G0
85(2)
6.3 Expansion of σ in V and G
87(2)
7 Transport Phenomena
89(18)
7.1 Boltzmann Equation Approach to Transport
90(8)
7.2 Green's Function Description of Transport
98(4)
7.3 Conservation Laws for g(U)
102(3)
7.4 Relation of g(U) to the Distribution Function f(p, R, T)
105(2)
8 Hartree Approximation, Collision-Less Boltzmann Equation, and Random Phase Approximation
107(22)
8.1 Collision-Less Boltzmann Equation
110(1)
8.2 Linearization of the Hartree Approximation: The Random Phase Approximation
111(3)
8.3 Coulomb Interaction
114(6)
8.4 Low-Temperature Fermion System and Zero Sound
120(4)
8.5 Breakdown of the Random Phase Approximation
124(5)
9 Relation between Real and Imaginary Time Response Functions
129(16)
9.1 Linear Response
129(6)
9.2 Continuation of Imaginary Time Response to Real Times
135(4)
9.3 Equations of Motion in the Real-Time Domain
139(6)
10 Slowly Varying Disturbances and the Boltzmann Equation
145(20)
10.1 Derivation of the Boltzmann Equation
146(7)
10.2 Generalization of the Boltzmann Equation
153(12)
11 Quasi-Equilibrium Behavior: Sound Propagation
165(20)
11.1 Complete Equilibrium Solutions
165(4)
11.2 Local Equilibrium Solutions
169(3)
11.3 Conservation Laws
172(2)
11.4 Application of Conservation Laws to the Quasi-Equilibrium Situation
174(6)
11.5 Sound Propagation
180(5)
12 The Landau Theory of the Normal Fermi Liquid
185(16)
12.1 The Boltzmann Equation
185(5)
12.2 Conservation Laws
190(5)
12.3 Thermodynamic Properties
195(6)
13 Shielded Potential
201(24)
13.1 Green's Function Approximation for Coulomb Gas
201(8)
13.2 Calculation of the Equation of State of a Coulomb Gas
209(16)
14 T Approximation
225(16)
14.1 Structure of the T Matrix
225(10)
14.2 Breakdown of the T Approximation in Metals
235(6)
Appendix A Finite-Temperature Perturbation Theory 241(10)
References and Supplementary Reading 251(4)
Index 255
In-Gee Kim is president of KimCNets, South Korea. He earned his PhD from Inha University, South Korea, in 2003, after which he worked with POSTECH, South Korea, as a post-doctoral researcher till 2005 and as an associate research professor till 2014. He was also with Northwestern University, Evanston, USA, as a post-doctoral research associate from 2004 to 2006. He moved to New Mexico Consortium, Inc., USA, in 2014 as associate research scientist and then to Lab021, LLC., South Korea, in 2016 as principal scientist. He was a research professor in Yonsei University, South Korea, till 2017.
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