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Ultracold Quantum Fields

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ISBN-10: 1402087624

ISBN-13: 9781402087622

Edition: 2009

Authors: Henk T. C. Stoof, Dennis B. M. Dickerscheid, Koos Gubbels

List price: $149.99
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'Ultracold Quantum Fields' provides a self-contained introduction to quantum field theory for many-particle systems, using functional methods throughout. The general focus is on the behaviour of so-called quantum fluids but trapped atomic gases are also used as an example.
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Book details

List price: $149.99
Copyright year: 2009
Publisher: Springer Netherlands
Publication date: 1/15/2009
Binding: Hardcover
Pages: 485
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 2.134
Language: English

Introduction
Ultracold Atomic Quantum Gases
Outline
Part 1
Part 2
Part 3
Gaussian Integrals
The Gaussian Integral over Real Variables
Generating Function
Multi-Dimensional Gaussian Integral
Complex Analysis
Differentiation and Contour Integrals
Laurent Series and the Residue Theorem
Gaussian Integrals over Complex Variables
Grassmann Variables
Problems
Quantum Mechanics
Hilbert Spaces
Observables
Schr�dinger vs. Heisenberg Picture
Bosonic Harmonic Oscillator
Creation and Annihilation Operators
Three-Dimensional Harmonic Oscillator
Coherent States
Fermionic Harmonic Oscillator
Spin
Perturbation Theory
Scattering Theory
Many-particle Quantum Mechanics
Problems
Statistical physics
Legendre Transformations
Statistical Physics
Spin Chain
Canonical Ensemble
Grand-Canonical Ensemble
Ideal Gases
Ideal Maxwell-Boltzmann Gas
Ideal Bose Gas: Bose-Einstein Condensation
Ideal Fermi Gas
Density Matrix
Problems
Path Integrals
Functionals and Functional Derivatives
Principle of Least Action
Phase-Space Representation
The Feynman Path Integral
Continuum Limit and Fluctuation Expansion
Gel'fand-Yaglom Method
Matrix Elements and Time Ordering
Quantum-Mechanical Partition Function
Expectation Values
Hubbard-Stratonovich Transformation
Problems
Second Quantization
Many-Body Hamiltonian
Fock Space
Creation and Annihilation Operators
Second-Quantized Hamiltonian
Field Operators
Equivalence of First and Second Quantization
Coherent States
Problems
Functional Integrals
Grand-Canonical Partition Function
Ideal Quantum Gases
Semiclassical Method
Matsubara Expansion
Green's Function Method
Wick's Theorem
Problems
Interactions and Feynman Diagrams
Quasiparticles
The Lehmann Representation
The Spectral-Weight Function
Collective Excitations
Perturbation Theory
Dyson's Equation
Hartree-Fock Approximation
Variational Approach
Hubbard-Stratonovich Transformation
Hartree Theory
Fock Theory
Hartree-Fock Theory for an Atomic Fermi Gas
The Jellium Model
Field-Theory Approach
Effective Action
Dispersion and Screened Coulomb Interaction
Problems
Landau Theory of Phase Transitions
Ising Model in d Dimensions
Landau Approach
Hubbard-Stratonovich Transformation
Gaussian Fluctuations
Spontaneous Symmetry Breaking
Problems
Atomic Physics
Atomic Structure
Fine Structure
Hyperfine Structure
Zeeman Effect
Two-body Scattering in Vacuum
Two-Body Transition Matrix
Partial-Wave Expansion
Scattering from a Square-Well Potential
Two-Body Scattering in a Medium
Physical Regimes
Problems
Bose-Einstein Condensation
Definitions for a Bose-Einstein Condensate
Superfluidity
Landau Criterion
Superfluid Density
Field-Theory Approach
Bogoliubov Theory and the Gross-Pitaevskii Equation
Dyson Equation
Quasiparticle Dispersion
Thermodynamic Potential for Bosons
Bogoliubov-de Gennes Equation
Popov Theory
Hydrodynamic-Like Approach
Time-Dependent Gross-Pitaevskii Equation
Collective Modes
Rotating Bose-Einstein Condensates
Attractive Interactions
Effective Action
Breathing Mode
Metastability of the Condensate
Problems
Condensation of Fermionic Pairs
Introduction
Thouless Criterion
Hubbard-Stratonovich Transformation
Bardeen-Cooper-Schrieffer Theory
Critical Temperature
Gap Equation
Thermodynamic Potential for Fermions
The BEC-BCS Crossover
Theoretical Results
Comparison with Experiment
Problems
Symmetries and Symmetry Breaking
Effective Actions
Noether's Theorem
Ward Identities
Hugenholtz-Pines Theorem
Bragg Scattering
RF Spectroscopy
Second-Order Perturbation Theory
Ladder Summations
Absence of Clock Shift
Absence of Vertex Corrections
Phase Diffusion
Problems
Renormalization Group Theory
The Renormalization-Group Transformation
Scaling
Interactions
Quantum Effects
Interactions
Nonuniversal Quantities
Renormalization Group for Fermions
Renormalization-Group Equations
Extremely-Imbalanced Case
Homogeneous Phase Diagram
Problems
Low-Dimensional Systems
Modified Popov Theory
Phase Fluctuations
Many-Body T Matrix
Long-Wavelength Physics
Comparison with Popo Theory
One Dimension
Two Dimensions
Three Dimensions
Vortices in Two Dimensions
Kosterlitz-Thouless Phase Transition
Trapped Bose Gases
Density Profiles
Phase Fluctuations
Comparision with Exact Results
Problems
Optical Lattices
Introduction
Coupling between Atoms and Light
Two-Level Approximation
Fine Structure
Band Structure
Hubbard Models
Superfluid-Mott Insulator Transition
Bogoliubov Approximation
Decoupling Approximation
Hubbard-Stratonovich Transformation
Fluctuations
Mott Insulator
Superfluid Phase
Bragg Spectroscopy
Problems
Feshbach Resonances
Example of a Feshbach Resonance
Bare Atom-Molecule Theory
Ladder Summations
Effective Atom-Molecule theory
Scattering Properties
Bound-State Energy
Molecular Density of States
Bogoliubov Theory for the Bose-Einstein Condensed Phase
Experiments
Josephson Frequency
Problems
References
Index