Quantum Many particle Systems 1st edition By John Negele, Henri Orland – Ebook PDF Instant Download/Delivery: 0738200521 , 9780738200521
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ISBN 10: 0738200521
ISBN 13: 9780738200521
Author: John Negele, Henri Orland
This book explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonperturbative approximations based on functional integrals; general arguments based on order parameters, symmetry, and Fermi liquid theory; and stochastic methods.
Quantum Many particle Systems 1st Table of contents:
Chapter 1 Second Quantization and Coherent States
1.1 Quantum Mechanics of a Single Particle
1.2 Systems of Identical Particles
1.3 Many-Body Operators
1.4 Creation and Annihilation Operators
1.5 Coherent States
Boson Coherent States
Grassmann Algebra
Fermion Coherent States
Gaussian Integrals
Problems for Chapter 1
Chapter 2 General Formalism at Finite Temperature
2.1 Introduction
Quantum Statistical Mechanics
Physical Response Functions and Green’s Functions
Approximation Strategies
2.2 Functional Integral Formulation
Feynman Path Integral
Imaginary-Time Path Integral and the Partition Function
Coherent State Functional Integral
The Partition Function for Many-Particle Systems
2.3 Perturbation Theory
Wick’s Theorem
Labeled Feynman Diagrams
Unlabeled Feynman Diagrams
Hugenholtz Diagrams
Frequency and Momentum Representation
The Linked Cluster Theorem
Calculation of Observables and Green’s functions
2.4 Irreducible Diagrams and Integral Equations
Generating Function for Connected Green’s Functions
The Effective Potential
The Self-Energy and Dyson’s Equation
Higher-Order Vertex Functions
2.5 Stationary-Phase Approximation and Loop Expansion
One-Dimensional Integral
Feynman Path Integral
Many-Particle Partition Function
Problems for Chapter 2
Chapter 3 Perturbation Theory at Zero Temperature
3.1 Feynman Diagrams
Observables
Zero-Temperature Fermion Propagators
Fermion Diagram Rules
Bosons
3.2 Time-Ordered Diagrams
3.3 The Zero-Temperature Limit
Problems for Chapter 3
Chapter 4 Order Parameters and Broken Symmetry
4.1 Introduction
Phases of Two Familiar Systems
Phenomenological Landau Theory
Broken Symmetry
4.2 General Formulation with Order Parameters
Infinite Range Ising Model
Generalizations
Physical Examples
4.3 Mean Field Theory
Legendre Transform
Ferromagnetic Transition for Classical Spins
Application to General Systems
4.4 Fluctuations
Landau Ginzburg Theory and Dimensional Analysis
One-Loop Corrections
Continuous Symmetry
One-Loop Corrections for the x – y model
Lower Critical Dimension
The Anderson-Higgs Mechanism
Problems for Chapter 4
Chapter 5 Green’s Functions
5.1 Introduction
Definitions
Evaluation of Observables
5.2 Analytic Properties
Zero Temperature Green’s Functions
Finite Temperature Green’s Functions
5.3 Physical Content of the Self Energy
Quasiparticle Pole
Effective Masses
Optical Potential
5.4 Linear Response
The Response Function
Random Phase Approximation
Zero Sound
Matrix Form of RPA
Sum Rules and Examples
5.5 Magnetic Susceptibility of a Fermi Gas
Static Susceptibility at Zero Temperature
Static Susceptibility at Finite Temperature
Dynamic Susceptibility at Zero Temperature
Dynamic Susceptibility at Finite Temperature
Problems for Chapter 5
Chapter 6 The Landau Theory of Fermi Liquids
6.1 Quasiparticles and their Interactions
6.2 Observable Properties of a Normal Fermi Liquid
Equilibrium Properties
Nonequilibrium Properties and Collective Modes
6.3 Microscopic Foundation
Calculation of the Quasiparticle Interaction
Problems for Chapter 6
Chapter 7 Further Development of Functional Integrals
7.1 Representations of the Evolution Operator
The Auxiliary Field
Overcomplete Sets of States
7.2 Ground State Properties for Finite Systems
The Resolvent Operator
Static Hartree Approximation
RPA Corrections
The Loop Expansion
7.3 Transition Amplitudes
S-Matrix Elements
7.4 Collective Excitations and Tunneling
Example of One Degree of Freedom
Eigenstates of Large Amplitude Collective Motion
Barrier Penetration and Spontaneous Fission
Conceptual Questions
7.5 Large Orders of Perturbation Theory
Study of a Simple Integral
Borel Summation
The Anharmonic Oscillator
Problems for Chapter 7
Chapter 8 Stochastic Methods
8.1 Monte Carlo Evaluation of Integrals
Central Limit Theorem
Importance Sampling
8.2 Sampling Techniques
Sampling Simple Functions
Markov Processes
Neumann-Ulam Matrix Inversion
Microcanonical Methods
8.3 Evaluation of One-Particle Path Integral
Observables
Sampling the Action
Initial Value Random Walk
Tunneling
8.4 Many Particle Systems
Path Integral in Coordinate Representation
Functional Integrals Over Fields
8.5 Spin Systems and Lattice Fermions
Checkerboard Decomposition
Special Methods for Spins
Problems for Chapter 8
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Tags: John Negele, Henri Orland, Quantum Many