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0 (hodnocen0 x )

BK

First edition

Weinheim : Wiley-VCH, [2020]

xvii, strana 1592-2353 : ilustrace ; 25 cm

ISBN 978-3-527-34555-7 (vázáno)

francouzština

Obsahuje bibliografii na stranách 2325-2331, bibliografické odkazy a rejstřík

001640384

VOLUME III // Table of contents v // XV CREATION AND ANNIHILATION OPERATORS FOR IDENTICAL PARTICLES 1591 // A General formalism ...1592 // One-particle symmetric operators ...1603 // Two-particle operators ...1608 // READER’S GUIDE FOR COMPLEMENTS 1617 // Axv Particles and holes 1621 // 1 Ground state of a non-interacting fermion gas ...1621 // 2 New definition for the creation and annihilation operators ...1622 // 3 Vacuum excitations ...1623 // Bxv Ideal gas in thermal equilibrium; quantum distribution functions 1625 // 1 Grand canonical description of a system without interactions ...1626 // 2 Average values of symmetric one-particle operators ...1628 // 3 Two-particle operators ...1631 // 4 Total number of particles ...1635 // 5 Equation of state, pressure ...1640 // Cxv Condensed boson system, Gross-Pitaevskii equation 1643 // 1 Notation, variational ket ...1643 // 2 First approach ...1645 // 3 Generalization, Dirac notation ...1648 // 4 Physical discussion ...1651 // Dxv Time-dependent Gross-Pitaevskii equation 1657 // 1 Time evolution ...1657 // 2 Hydrodynamic analogy ...1664 // 3 Metastable currents, superfluidity ...1667 // Exv Fermion system, Hartree-Fock approximation 1677 // 1 Foundation of the method ...1678 // 2 Generalization: operator method ...1688 // Fxv Fermions, time-dependent Hartree-Fock approximation 1701 // 1 Variational ket and notation ...1701 // 2 Variational method ...1702 // 3 Computing the optimizer ...1705 // 4 Equations of motion ...1707 // Gxv Fermions or Bosons: Mean field thermal equilibrium 1711 // 1 Variational principle ...1712 // 2 Approximation for the equilibrium density operator ...1716 // 3 Temperature dependent mean field equations ...1725 // Hxv Applications of the mean field method for non-zero temperature 1733 // 1 Hartree-Fock for non-zero temperature, a brief review ...1733 // 2 Homogeneous system ...1734 //

3 Spontaneous magnetism of repulsive fermions ...1737 // 4 Bosons: equation of state, attractive instability ...1745 // XVI FIELD OPERATOR 1751 // A Definition of the field operator ...1752 // B Symmetric operators ...1755 // C Time evolution of the field operator (Heisenberg picture) ...1763 // D Relation to field quantization ...1765 // READER’S GUIDE FOR COMPLEMENTS 1767 // Axvi Spatial correlations in an ideal gas of bosons or fermions 1769 // 1 System in a Fock state ...1769 // 2 Fermions in the ground state ...1771 // 3 Bosons in a Fock state ...1775 // Bxvi Spatio-temporal correlation functions, Green’s functions 1781 // 1 Green’s functions in ordinary space ...1781 // 2 Fourier transforms ...1790 // 3 Spectral function, sum rule ...1795 // Cxvi Wick’s theorem 1799 // 1 Demonstration of the theorem ...1799 // 2 Applications: correlation functions for an ideal gas ...1804 // XVII PAIRED STATES OF IDENTICAL PARTICLES 1811 // A Creation and annihilation operators of a pair of particles ...1813 // B Building paired states ...1818 // C Properties of the kets characterizing the paired states ...1822 // D Correlations between particles, pair wave function ...1830 // E Paired states as a quasi-particle vacuum; Bogolubov-Valatin transformations 1836 // READER’S GUIDE FOR COMPLEMENTS 1843 // Axvii Pair field operator for identical particles 1845 // 1 Pair creation and annihilation operators ...1846 // 2 Average values in a paired state ...1851 // 3 Commutation relations of field operators ...1861 // Bxvii Average energy in a paired state 1869 // 1 Using states that are not eigenstates of the total particle number ...1869 // 2 Hamiltonian ...1871 // 3 Spin 1/2 fermions in a singlet state ...1874 // 4 Spinless bosons ...1881 // Cxvii Fermion pairing, BCS theory 1889 // 1 Optimization of the energy ...1890 // 2 Distribution functions, correlations ...1899 //

3 Physical discussion ...1914 // 4 Excited states ...1919 // Dxvii Cooper pairs 1927 // 1 Cooper model ...1927 // 2 State vector and Hamiltonian ...1927 // 3 Solution of the eigenvalue equation ...1929 // 4 Calculation of the binding energy for a simple case ...1929 // Exvii Condensed repulsive bosons 1933 // 1 Variational state, energy ...1935 // 2 Optimization ...1937 // 3 Properties of the ground state ...1940 // 4 Bogolubov operator method ...1950 // XVIII REVIEW OF CLASSICAL ELECTRODYNAMICS 1957 // A Classical electrodynamics ...1959 // B Describing the transverse field as an ensemble of harmonic oscillators ...1968 // READER’S GUIDE FOR COMPLEMENTS 1977 // Axviii Lagrangian formulation of electrodynamics 1979 // 1 Lagrangian with several types of variables ...1980 // 2 Application to the free radiation field ...1986 // 3 Lagrangian of the global system field -f interacting particles ...1992 // XIX QUANTIZATION OF ELECTROMAGNETIC RADIATION 1997 // A Quantization of the radiation in the Coulomb gauge ...1999 // B Photons, elementary excitations of the free quantum field ...2004 // C Description of the interactions ...2008 // READER’S GUIDE FOR COMPLEMENTS 2017 // Axix Momentum exchange between atoms and photons 2019 // 1 Recoil of a free atom absorbing or emitting a photon ...2020 // 2 Applications of the radiation pressure force: slowing and cooling atoms ...2025 // 3 Blocking recoil through spatial confinement ...2036 // 4 Recoil suppression in certain multi-photon processes ...2040 // Bxix Angular momentum of radiation 2043 // 1 Average value of angular momentum for a spin 1 particle ...2044 // 2 Angular momentum of free classical radiation as a function of normal variables2047 // 3 Discussion ...2050 // Cxix Angular momentum exchange between atoms and photons 2055 // 1 Transferring spin angular momentum to internal atomic variables ...2056 //

2 Optical methods ...2058 // 3 Transferring orbital angular momentum to external atomic variables ...2065 // XX ABSORPTION, EMISSION AND SCATTERING OF PHOTONS BY ATOMS ...2067 // A A basic tool: the evolution operator ...2068 // B Photon absorption between two discrete atomic levels ...2073 // C Stimulated and spontaneous emissions ...2079 // D Role of correlation functions in one-photon processes ...2083 // E Photon scattering by an atom ...2085 // READER’S GUIDE FOR COMPLEMENTS 2095 // AXx A multiphoton process: two-photon absorption 2097 // 1 Monochromatic radiation ...2097 // 2 Non-monochromatic radiation ...2101 // 3 Discussion ...2105 // Bxx Photoionization 2109 // 1 Brief review of the photoelectric effect ...2110 // 2 Computation of photoionization rates ...2112 // 3 Is a quantum treatment of radiation necessary to describe photoionization? . 2117 // 4 Two-photon photoionization ...2123 // 5 Tunnel ionization by intense laser fields ...2126 // Cxx Two-level atom in a monochromatic field. Dressed-atom method 2129 // 1 Brief description of the dressed-atom method ...2130 // 2 Weak coupling domain ...2137 // 3 Strong coupling domain ...2141 // 4 Modifications of the field. Dispersion and absorption ...2147 // Dxx Light shifts: a tool for manipulating atoms and fields 2151 // 1 Dipole forces and laser trapping ...2151 // 2 Mirrors for atoms ...2153 // 3 Optical lattices ...2153 // 4 Sub-Doppler cooling. Sisyphus effect ...2155 // 5 Non-destructive detection of a photon ...2159 // Exx Detection of one- or two-photon wave packets, interference 2163 // 1 One-photon wave packet, photodetection probability ...2165 // 2 One- or two-photon interference signals ...2167 // 3 Absorption amplitude of a photon by an atom ...2174 // 4 Scattering of a wave packet ...2176 // 5 Example of wave packets with two entangled photons ...2181 //

XXI QUANTUM ENTANGLEMENT, MEASUREMENTS, BELL’S INEQUALITIES 2187 // A Introducing entanglement, goals of this chapter ...2188 // B Entangled states of two spin-1/2 systems ...2190 // C Entanglement between more general systems ...2193 // D Ideal measurement and entangled states ...2196 // E "Which path" experiment: can one determine the path followed by the photon in Young’s double slit experiment? ...2202 // F Entanglement, non-locality, Bell’s theorem ...2204 // READER’S GUIDE FOR COMPLEMENTS 2215 // Axxi Density operator and correlations; separability 2217 // 1 Von Neumann statistical entropy ...2217 // 2 Differences between classical and quantum correlations ...2221 // 3 Separability ...2223 // Bxxi GHZ states, entanglement swapping 2227 // 1 Sign contradiction in a GHZ state ...2227 // 2 Entanglement swapping ...2232 // Cxxi Measurement induced relative phase between two condensates 2237 // 1 Probabilities of single, double, etc. position measurements ...2239 // 2 Measurement induced enhancement of entanglement ...2242 // 3 Detection of a large number Q of particles ...2245 // Dxxi Emergence of a relative phase with spin condensates; macroscopic non-locality and the EPR argument 2253 // 1 Two condensates with spins ...2254 // 2 Probabilities of the different measurement results ...2255 // 3 Discussion ...2259 // APPENDICES 2267 // IV Feynman path integral 2267 // 1 Quantum propagator of a particle ...2267 // 2 Interpretation in terms of classical histories ...2272 // 3 Discussion; a new quantization rule ...2274 // 4 Operators ...2276 // V Lagrange multipliers 2281 // 1 Function of two variables ...2281 // 2 Function of N variables ...2283 // VI Brief review of Quantum Statistical Mechanics 2285 // 1 Statistical ensembles ...2285 // 2 Intensive or extensive physical quantities ...2292 // VII Wigner transform 2297 // 1 Delta function of an operator ...2299 //

2 Wigner distribution of the density operator (spinless particle) ...2299 // 3 Wigner transform of an operator ...2310 // 4 Generalizations ...2318 // 5 Discussion: Wigner distribution and quantum effects ...2319 // BIBLIOGRAPHY OF VOLUME III 2325 // INDEX 2333