Quantum Statistical Mechanics: Selected Works Of N N Bogolubov

by Nickolai N Bogolubov Jr

Overview

In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles.

Product Details

ISBN-13:	9789814612517
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/13/2014
Pages:	328
Product dimensions:	6.60(w) x 9.80(h) x 1.00(d)

Table of Contents

Foreword v

Part I 1

Chapter 1 On the Theory of Superfluidity 3

Chapter 2 Quasi-Averages in Problems of Statistical Mechanics 21

Part A Quasi-Averages 21

1 Green's Functions, Defined with Regular Averages; Additive Conservation Laws and Selection Rules 21

2 Degeneracy of the Statistical Equilibrium States; Introduction of Quasi-averages 25

3 Principle of Correlation Weakening 51

4 Particle Pair States 56

5 Certain Inequalities 63

Part B Characteristic Theorems about the 1/q² Type Interaction in the Theory of Superconductivity of Bose and Fermi Systems 68

6 Symmetry Properties of Basic Green's Functions for Bose Systems in the Presence of a Condensate 68

7 Model with a Condensate 73

8 The 1/q² Theorem and its Application 82

9 The 1/q² Theorem for Fermi Systems 92

Chapter 3 Hydrodynamics Equations in Statistical Mechanics 100

Chapter 4 On the Hydrodynamics of a Superfluid Liquid 123

Introduction 123

1 Preliminary Identities 124

2 Hydrodynamic Equations for a Normal Liquid 130

3 Hydrodynamic Equations for a Superfluid 140

4 Variational Equations and Green's Functions 157

Chapter 5 On the Model Hamiltonian of Superconductivity 168

1 Statement of the Problem 168

2 General Properties of the Hamiltonian 171

3 Upper Bound for the Minimum Eigenvalue of the Hamiltonian 176

4 Lower Bound for the Minimum Eigenvalue of the Hamiltonian 180

5 Green's Functions (Case ν > 0) 192

6 Green's Functions (Case ν = 0) 208

Appendix A 226

Appendix B The Principle of Extinction of Correlations 234

Part II 247

Chapter 6 Model Hamiltonians with Fermion Interaction 249

1 General Treatment of the Problem. Some Preliminary Results 250

2 Calculation of the Free Energy for Model System with Attraction 257

3 Further Properties of the Expressions for the Free Energy 269

4 Construction of Asymptotic Relations for the Free Energy 273

5 On the Uniform Convergence with Respect to θ of the Free Energy Function and on the Bounds for the Quantities δ_ν 279

6 Properties of Partial Derivatives of the Free Energy Function. Theorem 3 281

7 Rider to Theorem 3 and Construction of an Auxiliary Inequality 284

8 On the Difficulties of Introducing Quasi-Averages 288

9 A New Method of Introducing Quasi-Averages 292

10 The Question of the Choice of Sign for the Source-Terms 297

11 The Construction of Upper-Bound Inequalities in the Case C = 0 298

Additional References 306