Efnisyfirlit

• Cover
• Foreword
• Chapter XV: Creation and annihilation operators for identical particles
• A. General formalism
• B. One-particle symmetric operators
• C. Two-particle operators
• COMPLEMENTS OF CHAPTER XV, READER’S GUIDE
• Complement AXV Particles and holes
• 1. Ground state of a non-interacting fermion gas
• 2. New definition for the creation and annihilation operators
• 3. Vacuum excitations
• Complement BXV Ideal gas in thermal equilibrium; quantum distribution functions
• 1. Grand canonical description of a system without interactions
• 2. Average values of symmetric one-particle operators
• 3. Two-particle operators
• 4. Total number of particles
• 5. Equation of state, pressure
• Complement CXV Condensed boson system, Gross-Pitaevskii equation
• 1. Notation, variational ket
• 2. First approach
• 3. Generalization, Dirac notation
• 4. Physical discussion
• Complement DXV Time-dependent Gross-Pitaevskii equation
• 1. Time evolution
• 2. Hydrodynamic analogy
• 3. Metastable currents, superfluidity
• Complement EXV Fermion system, Hartree-Fock approximation
• 1. Foundation of the method
• 2. Generalization: operator method
• Complement FXV Fermions, time-dependent Hartree-Fock approximation
• 1. Variational ket and notation
• 2. Variational method
• 3. Computing the optimizer
• 4. Equations of motion
• Complement GXV Fermions or Bosons: Mean field thermal equilibrium
• 1. Variational principle
• 2. Approximation for the equilibrium density operator
• 3. Temperature dependent mean field equations
• Complement HXV Applications of the mean field method for non-zero temperature (fermions and bosons)
• 1. Hartree-Fock for non-zero temperature, a brief review
• 2. Homogeneous system
• 3. Spontaneous magnetism of repulsive fermions
• 4. Bosons: equation of state, attractive instability
• Chapter: XVI Field operator
• A. Definition of the field operator
• B. Symmetric operators
• C. Time evolution of the field operator (Heisenberg picture)
• D. Relation to field quantization
• COMPLEMENTS OF CHAPTER XVI, READER’S GUIDE
• Complement AXVI Spatial correlations in an ideal gas of bosons or fermions
• 1. System in a Fock state
• 2. Fermions in the ground state
• 3. Bosons in a Fock state
• Complement BXVI Spatio-temporal correlation functions, Green’s functions
• 1. Green’s functions in ordinary space
• 2. Fourier transforms
• 3. Spectral function, sum rule
• Complement CXVI Wick’s theorem
• 1. Demonstration of the theorem
• 2. Applications: correlation functions for an ideal gas
• Chapter: XVII Paired states particles of identical
• A. Creation and annihilation operators of a pair of particles
• B. Building paired states
• C. Properties of the kets characterizing the paired states
• D. Correlations between particles, pair wave function
• E. Paired states as a quasi-particle vacuum; Bogolubov-Valatin transformations
• COMPLEMENTS OF CHAPTER XVII, READER’S GUIDE
• Complement AXVII Pair field operator for identical particles
• 1. Pair creation and annihilation operators
• 2. Average values in a paired state
• 3. Commutation relations of field operators
• Complement BXVII Average energy in a paired state
• 1. Using states that are not eigenstates of the total particle number
• 2. Hamiltonian
• 3. Spin 1/2 fermions in a singlet state
• 4. Spinless bosons
• Complement CXVII Fermion pairing, BCS theory
• 1. Optimization of the energy
• 2. Distribution functions, correlations
• 3. Physical discussion
• 4. Excited states
• Complement DXVII Cooper pairs
• 1. Cooper model
• 2. State vector and Hamiltonian
• 3. Solution of the eigenvalue equation
• 4. Calculation of the binding energy for a simple case
• Complement EXVII Condensed repulsive bosons
• 1. Variational state, energy
• 2. Optimization
• 3. Properties of the ground state
• 4. Bogolubov operator method
• Chapter: XVIII REVIEW OF CLASSICAL ELECTRODYNAMICS
• A. Classical electrodynamics
• B. Describing the transverse field as an ensemble of harmonic oscillators
• COMPLEMENTS OF CHAPTER XVIII, READER’S GUIDE
• Complement AXVIII Lagrangian formulation of electrodynamics
• 1. Lagrangian with several types of variables
• 2. Application to the free radiation field
• 3. Lagrangian of the global system field + interacting particles
• Chapter: XIX QUANTIZATION OF ELECTROMAGNETIC RADIATION
• A. Quantization of the radiation in the Coulomb gauge
• B. Photons, elementary excitations of the free quantum field
• C. Description of the interactions
• COMPLEMENTS OF CHAPTER XIX, READER’S GUIDE
• Complement AXIX Momentum exchange between atoms and photons
• 1. Recoil of a free atom absorbing or emitting a photon
• 2. Applications of the radiation pressure force: slowing and cooling atoms
• 3. Blocking recoil through spatial confinement
• 4. Recoil suppression in certain multi-photon processes
• Complement BXIX Angular momentum of radiation
• 1. Quantum average value of angular momentum for a spin 1 particle
• 2. Angular momentum of free classical radiation as a function of normal variables2047
• 3. Discussion
• Complement CXIX Angular momentum exchange between atoms and photons
• 1. Transferring spin angular momentum to internal atomic variables
• 2. Optical methods
• 3. Transferring orbital angular momentum to external atomic variables
• Chapter: XX ABSORPTION, EMISSION AND SCATTERING OF PHOTONS BY ATOMS
• A. A basic tool: the evolution operator
• B. Photon absorption between two discrete atomic levels
• C. Stimulated and spontaneous emissions
• D. Role of correlation functions in one-photon processes
• E. Photon scattering by an atom
• COMPLEMENTS OF CHAPTER XX, READER’S GUIDE
• Complement AXX A multiphoton process: two-photon absorption
• 1. Monochromatic radiation
• 2. Non-monochromatic radiation
• 3. Discussion
• Complement BXX Photoionization
• 1. Brief review of the photoelectric effect
• 2. Computation of photoionization rates
• 3. Is a quantum treatment of radiation necessary to describe photoionization? .
• 4. Two-photon photoionization
• 5. Tunnel ionization by intense laser fields
• Complement CXX Two-level atom in a monochromatic field. Dressed-atom method
• 1. Brief description of the dressed-atom method
• 2. Weak coupling domain
• 3. Strong coupling domain
• 4. Modifications of the field. Dispersion and absorption
• Complement DXX Light shifts: a tool for manipulating atoms and fields
• 1. Dipole forces and laser trapping
• 2. Mirrors for atoms
• 3. Optical lattices
• 4. Sub-Doppler cooling. Sisyphus effect
• 5. Non-destructive detection of a photon
• Complement EXX Detection of one- or two-photon wave packets, interference
• 1. One-photon wave packet, photodetection probability
• 2. One- or two-photon interference signals
• 3. Absorption amplitude of a photon by an atom
• 4. Scattering of a wave packet
• 5. Example of wave packets with two entangled photons
• Chapter: XXI QUANTUM ENTANGLEMENT, MEASUREMENTS, BELL’S INEQUALITIES
• A. Introducing entanglement, goals of this chapter
• B. Entangled states of two spin-1/2 systems
• C. Entanglement between more general systems
• D. Ideal measurement and entangled states
• E. “Which path” experiment: can one determine the path followed by the photon in Young’s double slit experiment?
• F. Entanglement, non-locality, Bell’s theorem
• COMPLEMENTS OF CHAPTER XXI, READER’S GUIDE
• Complement AXXI Density operator and correlations; separability
• 1. Von Neumann statistical entropy
• 2. Differences between classical and quantum correlations
• 3. Separability
• Complement BXXI GHZ states, entanglement swapping
• 1. Sign contradiction in a GHZ state
• 2. Entanglement swapping
• Complement CXXI Measurement induced relative phase between two condensates
• 1. Probabilities of single, double, etc. position measurements
• 2. Measurement induced enhancement of entanglement
• 3. Detection of a large number Q of particles
• Complement DXXI Emergence of a relative phase with spin condensates; macroscopic non-locality and the EPR argument
• 1. Two condensates with spins
• 2. Probabilities of the different measurement results
• 3. Discussion
• Appendix IV: Feynman path integral
• 1. Quantum propagator of a particle
• 2. Interpretation in terms of classical histories
• 3. Discussion; a new quantization rule
• 4. Operators
• Appendix V: Lagrange multipliers
• 1. Function of two variables
• 2. Function of AT variables
• Appendix VI: Brief review of Quantum Statistical Mechanics
• 1. Statistical ensembles
• 2. Intensive or extensive physical quantities
• Appendix VII: Wigner transform
• 1. Delta function of an operator
• 2. Wigner distribution of the density operator (spinless particle)
• 3. Wigner transform of an operator
• 4. Generalizations
• 5. Discussion: Wigner distribution and quantum effects
• Bibliography of volume III
• Index
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