A Method for Studying Model Hamiltonians

A Method for Studying Model Hamiltonians

A Minimax Principle for Problems in Statistical Physics

1st Edition - January 1, 1972

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  • Author: N. N. Bogolyubov
  • eBook ISBN: 9781483148779

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Description

A Method for Studying Model Hamiltonians: A Minimax Principle for Problems in Statistical Physics centers on methods for solving certain problems in statistical physics which contain four-fermion interaction. Organized into four chapters, this book begins with a presentation of the proof of the asymptotic relations for the many-time correlation functions. Chapter 2 details the construction of a proof of the generalized asymptotic relations for the many-time correlation averages. Chapter 3 explains the correlation functions for systems with four-fermion negative interaction. The last chapter shows the model systems with positive and negative interaction components.

Table of Contents


  • Series Editor's Preface

    Preface

    Introduction

    § 1. General Remarks

    § 2. Remarks an Quasi-Averages

    Chapter 1. Proof of the Asymptotic Relations for the Many-Time Correlation Functions

    § 1. General Treatment of the Problem. Some Preliminary Results and Formulation of the Problem

    § 2. Equations of Motion and Auxiliary Operator Inequalities

    § 3. Additional Inequalities

    § 4. Bounds for the Difference of the Single-Time Averages

    § 5. Remark (I)

    § 6. Proof of the Closeness of Averages Constructed on the Basis of Model and Trial Hamiltonians for "Normal" Ordering of the Operators in the Averages

    § 7. Proof of the Closeness of the Averages for Arbitrary Ordering of the Operators in the Averages

    Remark (II)

    § 8. Estimates of the Asymptotic Closeness of the Many-Time Correlation Averages

    Chapter 2. Construction of a Proof of the Generalized Asymptotic Relations for the Many-Time Correlation Averages

    § 1. Selection Rules and Calculation of the Averages

    § 2. Generalized Convergence

    § 3. Remark

    § 4. Proof of the Asymptotic Relations

    § 5. Remark on the Construction of Uniform Bounds

    § 6. Generalized Asymptotic Relations for the Green's Functions

    § 7. The Existence of Generalized Limits

    Chapter 3. Correlation Functions for Systems with Four-Fermion Negative Interaction

    § 1. Calculation of the Free Energy for Model Systems with Attraction

    § 2. Further Properties of the Expressions for the Free Energy

    § 3. Construction of Asymptotic Relations for the Free Energy

    § 4. On the Uniform Convergence with Respect to θ of the Free Energy Function and on Bounds for the Quantities δv

    § 5. Properties of Partial Derivatives of the Free Energy Function. Theorem 3.III

    § 6. Rider to Theorem 3.III and Construction of an Auxiliary Inequality

    § 7. On the Difficulties of Introducing Quasi-Averages

    § 8. A New Method of Introducing Quasi-Averages

    § 9. The Question of the Choice of Sign for the Source-Terms

    § 10. The Construction of Upper-Bound Inequalities in the Case When C=0

    Chapter 4. Model Systems with Positive and Negative Interaction Components

    § 1. Hamiltonian with Negative Coupling Constants (Repulsive Interaction)

    § 2. Features of the Asymptotic Relations for the Free Energies in the Case of Systems with Positive Interaction

    § 3. Bounds for the Free Energies and Correlation Functions

    § 4. Examination of an Auxiliary Problem

    § 5. Solution of the Question of Uniqueness

    § 6. Hamiltonians with Coupling Constants of Different Signs. The Minimax Principle

    References

    Index

Product details

  • No. of pages: 180
  • Language: English
  • Copyright: © Pergamon 1972
  • Published: January 1, 1972
  • Imprint: Pergamon
  • eBook ISBN: 9781483148779

About the Author

N. N. Bogolyubov

About the Editor

D. ter Haar

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