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Modern Many-Particle Physics: Atomic Gases, Nanostructures and Quantum Liquids

E. Lipparini

Published Jan 2, 2008• 14 citations
OpenAlex

Abstract

Independent-Particle Model The Hartree-Fock Theory The Brueckner-Hartree-Fock (BHF) Theory The Density Functional Theory (DFT) The Confined 2D Electron Gas in a Magnetic Field Spin-Orbit Coupling in Confined 2D Electron Gas Monte Carlo Methods The Linear Response Function Theory The Linear Response Function in Different Models Dynamic Correlations and Response Function The Hydrodynamic and Elastic Models.

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Many-Particle Theory,

Eberhard K. U. Gross, E. Runge, Olle Heinonen

Part 1 Fundamentals and examples: systems of identical particles second quantization for fermions second quantization for bosons unitary transformations and field operators example - the Hamiltonian of translationally invariant systems in second quantization density operators the Hartree-Fock approximation restricted Hartree-Fock approximation and the symmetry dilemma Hartree-Fock for translationally invariant systems the homogeneous electron gas in the Hartree-Fock approximation long-range correlations in the electron-gas - plasmons phonons superconductivity. Part 2 Green's functions: pictures the single-particle Green's function and the hierarchy of equations of motion. Part 3 Perturbation theory: time-dependent perturbation theory with adiabatic turning-on of the interaction particle and hole operators and Wick's theorem Feynman diagrams diagrammatic calculation of the vacuum amplitude an example - the Gell-Mann-Brueckner correlation energy of a dense electron gas diagrammatic calculation of the single-particle Green's function - Dyson's equation diagrammatic analysis of the Green's function G(kappa, omega) self-consistent perturbation theory, higher-order Hartree-Fock theory the quasi-particle concept diagrammatic calculation of the two-particle Green's function and the polarization propagator effective interaction and dressed vertices plasmons in higher order perturbation theory at finite temperatures. Part 4 Fermi liquid theory: introduction equilibrium properties transport equation and collective modes microscopic derivation of the Landau fermi liquid theory applications to the Kondo problem.

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Many-body physics in condensed matter systems

Marco Polini, Mario P. Tosi

This volume collects the lecture notes of an introductory course on the theory of many-body systems, held at the Scuola Normale Superiore di Pisa. It is mainly addressed to fourth and fifth-year undergraduates and to first-year graduates in physics and chemistry. The book is also suitable for researchers in the field wanting to gain a general introductory overview on its modern focal points. Starting from a set of notes first prepared in 1994, which were mainly focused on conduction electrons in metals and semiconductors, these lecture notes are now being reprinted with some major changes and additions in order to provide the reader with an overview of recent developments in the understanding of low-dimensional electron fluids and of confined quantum gases made from bosonic and fermionic atoms and molecules.The book is divided into seven chapters and includes 18 appendices on specialized topics. The introductory chapter illustrates some of the longstanding problems in many-body physics. Chapters 2, 3 and 4 are mainly devoted to topics concerning electron fluids. A formal presentation of the theory of Green's functions and linear response functions for fermions in chapter 2 is followed by a chapter on electron liquids in the normal state and by a further chapter on the magnetism of conduction electrons and strongly correlated electron fluids. Chapter 5 turns to the formal theory of Green's functions and linear response functions for bosons. And finally, Chapters 6 and 7 are on trapped boson gases and on confined fermion gases and gaseous boson-fermion mixtures.

•Oct 1, 2006•4 citations

A microscopic study of spin-polarized neutron matter

Mohamed K. Al-Sugheir, F.F. Mqbel

In this work, the static fluctuation approximation (SFA) is used to investigate the thermodynamic properties of spin-polarized neutron matter. The energy per particle, pressure, entropy per particle, specific heat capacity, and effective magnetic field are studied as functions of density, temperature, and polarization fraction. The Argonne v18 nucleon–nucleon potential is used here. It is found that the energy per particle, pressure, entropy per particle, and effective magnetic field increase as the density or temperature increases. Also, the energy per particle and pressure are linearly dependent on the quadratic spin polarization δ2. The system becomes more ordered as δ increases. Our calculations are found to be in good agreement with previously published results obtained with different many-body techniques, such as the lowest order constrained variational (LOCV) method, the Brueckner–Hartree–Fock (BHF) approach, and the Dirac–Brueckner–Hartree–Fock (DBHF) technique.

Canadian Journal of Physics•Aug 4, 2021•1 citation

Many-body quantum theory in condensed matter physics - an introduction

Henrik Bruus, Karsten Flensberg

1. First and second quantization 2. The electron gas 3. Phonons: coupling to electrons 4. Mean field theory 5. Time evolution pictures 6. Linear response theory 7. Transport in mesoscopic systems 8. Green's functions 9. Equation of motion theory 10. Transport in interacting mesoscopic systems 11. Imaginary time Green's functions 12. Feynman diagrams and external potentials 13. Feynman diagrams and pair interactions 14. The interacting electron gas 15. Fermi liquid theory 16. Impurity scattering and conductivity 17. Green's functions and phonons 18. Superconductivity 19. 1D electron gases and Luttinger liquids A. Fourier transformations B. Exercises C. Index

Oxford University Press eBooks•Jan 1, 2004•254 citations
Independent-Particle Model The Hartree-Fock Theory The Brueckner-Hartree-Fock (BHF) Theory The Density Functional Theory (DFT) The Confined 2D Electron Gas in a Magnetic Field Spin-Orbit Coupling in Confined 2D Electron Gas Monte Carlo Methods The Linear Response Function Theory The Linear Response Function in Different Models Dynamic Correlations and Response Function The Hydrodynamic and Elastic Models.
Part 1 Fundamentals and examples: systems of identical particles second quantization for fermions second quantization for bosons unitary transformations and field operators example - the Hamiltonian of translationally invariant systems in second quantization density operators the Hartree-Fock approximation restricted Hartree-Fock approximation and the symmetry dilemma Hartree-Fock for translationally invariant systems the homogeneous electron gas in the Hartree-Fock approximation long-range correlations in the electron-gas - plasmons phonons superconductivity. Part 2 Green's functions: pictures the single-particle Green's function and the hierarchy of equations of motion. Part 3 Perturbation theory: time-dependent perturbation theory with adiabatic turning-on of the interaction particle and hole operators and Wick's theorem Feynman diagrams diagrammatic calculation of the vacuum amplitude an example - the Gell-Mann-Brueckner correlation energy of a dense electron gas diagrammatic calculation of the single-particle Green's function - Dyson's equation diagrammatic analysis of the Green's function G(kappa, omega) self-consistent perturbation theory, higher-order Hartree-Fock theory the quasi-particle concept diagrammatic calculation of the two-particle Green's function and the polarization propagator effective interaction and dressed vertices plasmons in higher order perturbation theory at finite temperatures. Part 4 Fermi liquid theory: introduction equilibrium properties transport equation and collective modes microscopic derivation of the Landau fermi liquid theory applications to the Kondo problem.
This volume collects the lecture notes of an introductory course on the theory of many-body systems, held at the Scuola Normale Superiore di Pisa. It is mainly addressed to fourth and fifth-year undergraduates and to first-year graduates in physics and chemistry. The book is also suitable for researchers in the field wanting to gain a general introductory overview on its modern focal points. Starting from a set of notes first prepared in 1994, which were mainly focused on conduction electrons in metals and semiconductors, these lecture notes are now being reprinted with some major changes and additions in order to provide the reader with an overview of recent developments in the understanding of low-dimensional electron fluids and of confined quantum gases made from bosonic and fermionic atoms and molecules.The book is divided into seven chapters and includes 18 appendices on specialized topics. The introductory chapter illustrates some of the longstanding problems in many-body physics. Chapters 2, 3 and 4 are mainly devoted to topics concerning electron fluids. A formal presentation of the theory of Green's functions and linear response functions for fermions in chapter 2 is followed by a chapter on electron liquids in the normal state and by a further chapter on the magnetism of conduction electrons and strongly correlated electron fluids. Chapter 5 turns to the formal theory of Green's functions and linear response functions for bosons. And finally, Chapters 6 and 7 are on trapped boson gases and on confined fermion gases and gaseous boson-fermion mixtures.
In this work, the static fluctuation approximation (SFA) is used to investigate the thermodynamic properties of spin-polarized neutron matter. The energy per particle, pressure, entropy per particle, specific heat capacity, and effective magnetic field are studied as functions of density, temperature, and polarization fraction. The Argonne v18 nucleon–nucleon potential is used here. It is found that the energy per particle, pressure, entropy per particle, and effective magnetic field increase as the density or temperature increases. Also, the energy per particle and pressure are linearly dependent on the quadratic spin polarization δ2. The system becomes more ordered as δ increases. Our calculations are found to be in good agreement with previously published results obtained with different many-body techniques, such as the lowest order constrained variational (LOCV) method, the Brueckner–Hartree–Fock (BHF) approach, and the Dirac–Brueckner–Hartree–Fock (DBHF) technique.
1. First and second quantization 2. The electron gas 3. Phonons: coupling to electrons 4. Mean field theory 5. Time evolution pictures 6. Linear response theory 7. Transport in mesoscopic systems 8. Green's functions 9. Equation of motion theory 10. Transport in interacting mesoscopic systems 11. Imaginary time Green's functions 12. Feynman diagrams and external potentials 13. Feynman diagrams and pair interactions 14. The interacting electron gas 15. Fermi liquid theory 16. Impurity scattering and conductivity 17. Green's functions and phonons 18. Superconductivity 19. 1D electron gases and Luttinger liquids A. Fourier transformations B. Exercises C. Index