Modern Many-Particle Physics

The following sections are included:

• Preface

• Preface to the Second Edition

• Contents

The following sections are included:

• Introduction

• Bosons

• Fermions

• Matrix Elements of One-Body Operators

• Matrix Elements of Two-Body Operators

• Density Matrices

• The Ideal Bose Gas Confined in a Harmonic Potential

• The Fermi Gas
  • Excited States
  • Polarized Fermi Gas
  • The Fermi Gas in Two Dimensions with Rashba Interaction

• Finite Temperature and Quasiparticles

• References

The following sections are included:

• Introduction

• The Hartree–Fock Method for Fermions
  • Examples of Physical Systems Treated by the Hartree–Fock Method
  • Examples of Infinite Systems Treated by the Hartree–Fock Method

• The Hartree–Fock Method for Bosons

• The Gross–Pitaevskii Equations

• Hartree–Fock in Second Quantization Language

• Hartree–Fock at Finite Temperature

• Hartree–Fock–Bogoliubov and BCS

• Appendix: Second Quantization

• References

The following sections are included:

• Introduction

• The Lippman–Schwinger Equation

• The Bethe–Goldstone Equation

• Examples of Application of the BHF Theory
  • The One-Dimensional Fermion System
  • Ultracold Highly Polarized Fermi Gases

• Numerical Results of BHF Calculation in Different Systems

• The g Matrix for the 2D Electron Gas
  • Decomposition in Partial Waves
  • The Separable Approximation
  • The g Matrix Expansion
  • Numerical Results and Discussion

• The g Matrix for Confined Electron Systems
  • Effective Interaction in Confined Electron Systems

• The BBP Method
  • Appendix

• References

The following sections are included:

• Introduction

• The Density Functional Formalism

• Examples of Application of the Density Functional Theory
  • The Thomas–Fermi Theory for the Atom
  • The Gross–Pitaevskii Theory for the Ground State of a Dilute Gas of Bosons
  • The Thomas–Fermi Approximation for the Fermi Gas Confined in a Harmonic Potential

• The Kohn–Sham Equations

• The Local Density Approximation for the Exchange-Correlation Energy

• The Local Spin Density Approximation (LSDA)

• Inclusion of Current Terms in the DFT (CDFT)

• The Ensemble Density Functional Theory (EDFT)

• The DFT for Strongly Correlated Systems: Nuclei and Helium

• The DFT for Mixed Systems

• Symmetries and Mean Field Theories

• References

The following sections are included:

• Introduction

• Quantum Dots in a Magnetic Field
  • The ω₀ ≫ ω_c Case
  • The ω_c ≫ ω₀ Case
  • The Maximum Density Droplet (MDD) State

• The Fractional Regime

• The Hall Effect

• Elliptical Quantum Dots
  • Analogies with the Bose–Einstein Condensate in a Rotating Trap

• The DFT for Quantum Dots in a Magnetic Field

• Quantum Wires

• The Aharanov–Bohm Effect and Quantum Rings

• Quantum Molecules
  • The B = 0 Case
  • B ≠ 0

• References

The following sections are included:

• Spin–Orbit Coupling in Semiconductors

• Spin–Orbit Effects on Single-Particle States in Quantum Wells
  • The Case in Which Either λ_R = 0 or λ_D = 0
  • The General Case Where λ_R ≠ 0 and λ_D ≠ 0

• Single-Particle Level Transitions in Quantum Wells

• The Magnetic Field in Plane

• Spin–Orbit Effects on Single-Particle States in Quantum Dots
  • Single-Particle Transitions in Dots

• Spin–Orbit Effects on Single-Particle States in Quantum Wires

• The LSDA with Spin–Orbit Coupling

• Comparison with Experiments in Quantum Wells

• LSDA Results and Comparison with Experiments for Quantum Dots

• LSDA Results for Quantum Wires

• Appendix A

• Appendix B

• References

The following sections are included:

• Introduction

• Standard Quadrature Methods

• Random Variable Distributions and the Central Limit Theorem

• Sampling Techniques
  • The Inversion Rule
  • The Rejection Method
  • Markov Chains

• The Metropolis Algorithm [M(RT)²]

• Variational Monte Carlo for Liquid ⁴He

• Variational Monte Carlo for Fermions

• Optimization of Variational Wave Functions

• Monte Carlo Methods and Quantum Mechanics

• Propagation of a State in Imaginary Time

• The Schrödinger Equation in Imaginary Time

• Importance Sampling

• Importance Sampling and Green Functions

• Fermion Systems and the Sign Problem

• Two Examples of DMC Calculations in Many-Body Systems
  • The Equation of State of Diluted Ultracold Fermi Gases in the BEC–BCS Crossover
  • Many-Nucleon Systems

• References

The following sections are included:

• Introduction

• The General Formalism

• The Linear Response Function and Sum Rules

• Finite Temperature

• The Density Response

• The Density Response for Noninteracting Homogeneous Systems

• The Current Response to an Electromagnetic Field

• The Conductivity of Quantum Wires

• Magnetoconductivity
  • The Kohn Theorem
  • Magnetoconductivity and the Quantum Hall Effect

• The Larmor Theorem
  • Electron Spin Precession with Rashba Spin–Orbit Coupling

• Deviations from Kohn and Larmor Theorems Due to Spin–Orbit Coupling
  • Spin–Orbit Splitting of Cyclotron Resonance
  • Spin Splitting of Landau Levels

• Spin-Hall Conductivity
  • The Spin-Hall Effect at a Finite Magnetic Field
  • Spin-Hall Conductivity Without SO Coupling
  • Influence of the SO Coupling on the Spin-Hall Conductivity

• Hall Conductivity in Graphene

• References

The following sections are included:

• The Linear Response Function in Landau Theory

• Time Dependent Hartree (TDH) for Homogeneous Systems: The RPA

• TDH for the Density Matrix and the Landau Equations

• The RPA for the Electron Gas in Different Dimensions: The Plasmon

• The RPA for Bosons

• The Time-Dependent Gross–Pitaevskii Theory

• Time-Dependent Hartree–Fock (TDHF) and the Matrix RPAE

• Examples of Application of the RPA Theory
  • The RPA with Separable Interactions
  • The RPAE for metal clusters

• The Adiabatic Time-Dependent LSDA (TDLSDA)
  • The TDLSDA Longitudinal Response Function
  • The TDLSDA Transverse Response Function

• RPA and TDLSDA Commutators and Symmetry Restoration

• The Linear Response Based on the Green Functions; RPAE

• The Screened Response Function and the Dielectric Constant

• Examples of Application of the TDLSDA Theory
  • Quantum Wells under a Very High External Magnetic Field
  • Quantum Dots Under Magnetic Field

• References

The following sections are included:

• Introduction

• Interaction Energy and Correlation Energy

• The RPA Correlation Energy
  • The RPA Correlation Energy for the Cold and Dilute Gas of Bosons and Fermions

• Theories Beyond the RPA

• The STLS Theory

• Comparison of Different Theories for the Electron Gas in 2D

• Quasiparticle Properties

• Nonlocal Effects

• Mean Energy of Many-Particle Excitations

• The Polarization Potential Model

• The Gross–Kohn Model

• The Method of Lorentz Transforms

• References

The following sections are included:

• The Hydrodynamic Model for Bosons
  • Backflow
  • Compression and Surface Modes of Spherical Drops
  • Compression and Surface Modes of a Bose Gas in a Magnetic Trap
  • Compression and Surface Modes of a Superfluid Trapped Fermi Gas
  • The Moment of Inertia and the Scissor Mode of a Bose Gas in a Magnetic Trap
  • Vortices in the Bose Gas in a Magnetic Trap

• The Fluidodynamic and Hydrodynamic Model for Fermions
  • Dipolar Modes in Metal Clusters
  • Spin Oscillations in Trapped Fermi Gases
  • The Scalar Quadrupole Mode in Confined Systems
  • The Scissor Mode in Fermi Systems
  • The Moment of Inertia of Quantum Dots
  • The Vibrating Potential Model

• The Surface Vibrations of Charged Systems in 2D and 3D
  • Surface Vibrations of Charged Metal Clusters
  • Edge Vibrations of Quantum Dots

• References

The following sections are included:

• Index