Aspects Of Polaron Theory: Equilibrium And Nonequilibrium Problems

by Nickolai N Bogolubov Jr, N N Bogolubov

Overview

The linear polaron model is an excellent example of an exactly soluble, yet nontrivial polaron system. It serves as a trial system or zero-level approximation in many sophisticated methods of polaron investigation. This book analyzes, in particular, the possibility of reduction of the full polaron Hamiltonian to the linear one, and introduces a special method of calculating thermodynamical characteristics based on the calculation of the averages of T-products. This T-product formalism seems to be a more convenient way of doing similar calculations involving Feynman's path integral approach.This book follows a step-by-step approach, from comparatively simple physical ideas to a clear understanding of sophisticated mathematical tools of investigation in modern polaron physics. The reader is able to compare the physical point of view with methods proposed in the book, and at the same time grasp the underlying mathematics.Some familiarity with quantum statistical mechanics is desirable in reading this book.

Product Details

ISBN-13:	9789812833983
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/30/2008
Pages:	180
Product dimensions:	6.10(w) x 9.00(h) x 0.70(d)

Table of Contents

Introduction 3

Chapter 1 Linear Polaron Model 15

1.1 Introduction to the Linear Polaron Model 15

1.2 Equations of Motion 18

1.3 Two-time Correlation Functions and Green Functions for the Linear Polaron Model 21

1.4 Free Energy Calculation for the Linear Polaron Model 32

1.5 Average Values of T-products 42

1.6 Averaged Operator T-Product Calculus for Some Model Oscillatory Systems 45

1.7 Auxiliary Operator Identities 60

Chapter 2 Equilibrium Thermodynamic State of Polaron System 63

2.1 Free Energy and Ground State Energy Calculation 63

2.2 Equilibrium Momentum Distribution Function in the Polaron Theory 93

Chapter 3 Kinetic Equations in Polaron Theory 117

3.1 Generalized Kinetic Equation. Method of Rigorous Bose-Amplitude Elimination 118

3.2 Kinetic Equations in the First-Order Approximation for Weak Interactions 128

3.3 Nonequilibrium Properties of the Linear Polaron Model 135

Appendix I 163

Appendix II 167

Appendix III 171

References 173