## Statistical Physics, Part 2The second part of 'Statistical Physics' deals with the quantum theory of the condensed state of matter. This volume is essentially an entirely new book, based on the large amount of new material which has become available in statistical physics since' Part 1' was published. |

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### Contents

THE NORMAL FERMI LIQUID 1 Elementary exitattons in a quantum Fermi liquid | 1 |

Interaction of quasipar tides | 8 |

Magnetic susceptibility of a Fermi liquid | 12 |

Zero sound | 13 |

Spin waves in a Fermi liquid | 19 |

A degenerate almost ideal Feimi gas with repulsion between the particles | 21 |

Greens functions in a macroscopic system | 28 |

Determination of the enregy spectrum from the Greens function | 33 |

The structure of the mixed state | 193 |

I iamagnetic susceptibility above the transition point | 201 |

The Josephson effect | 204 |

Relation between current and magnetic field in a superconductor | 208 |

Depth of penetration of a magnetic field into a superconductor | 214 |

Superconducting alloys | 216 |

The Cooper effect for nonzero orbital angular momenta of the pair | 219 |

ELECTRONS IN THE CRYSTAL LATTICE 55 An electron in a periocid field | 223 |

Greens function of an ideal Fermi gas | 38 |

Particle momentum distribution in a Fermi liquid | 41 |

Calculation of thermodynamic quantities from the Greens function | 42 |

P operators in the interaction representation | 43 |

The diagram technique for Fermi systems | 46 |

The selfenergy function | 53 |

The twoparticle Greens function | 56 |

The relation of the vertex function of the quasiparticle scattering amplitude | 60 |

The vertex function for small momentum transfers | 63 |

The relation of t he vertex function to the quasipai tide interaction function | 68 |

Identities for derivatives of the Greens function | 71 |

Derivation of the relation between the limiting momentum and the density | 76 |

Greens function of an almost ideal Fermi gas | 78 |

SUPERFLUIDITY 22 Elementary excitations in a quantum Bose liquid | 85 |

Superfluidity U 24 Phonons in a liquid | 95 |

A degenerate almost ideal Bose gas | 98 |

The wave function of the condensate | 102 |

Temperature dependence of the condensate density | 106 |

Behaviour of the superfluid density near the Apoim | 109 |

Quantized vortex filaments | 111 |

A vortex filament in an almost ideal Bose gas | 117 |

Greens functions in a Bose liquid | 118 |

The diagram technique for a Bose liquid | 125 |

Sellenergy functions | 127 |

Disintegration of quasipanicles | 131 |

Properties of the spectrum near its termination point | 135 |

GREENS FUNCTIONS AT NONZERO TEMPERATURES 36 Greens functions at nonzero temperatures | 141 |

Temperature Greens functions | 146 |

The diagram technique for temperature Greens functions | 149 |

SUPERCONDUCTIVITY 39 A superfluid Fermi gas The energy spectrum | 153 |

A superfluid Fermi gas Thermodynamic properties | 163 |

Greens functions in a supcrfluid Fermi gas | 164 |

Temperature Greens functions in a superfluid Fermi gas | 169 |

Superconductivity in metals | 171 |

The superconductivity current | 173 |

The GinzburgLandau equations | 178 |

Surface tension at the boundary of superconducting and normal phases | 184 |

The two types of superconductor | 190 |

Effect of an external fied on electron motion in a lattice | 232 |

Quasiclassical traiectories | 236 |

Quasiclassical energy levels | 240 |

The electron effective mass tensor in the lattice | 243 |

Symmetry of electron states in a lattice in a magnetic field | 247 |

Electronic spectra of normal metals | 251 |

Greens function of electrons in a metal | 255 |

The de Haasvan Alphen effect | 259 |

Electronphonon interaction | 266 |

Effect of the electronphonon interaction on the electron spectrum in a metal | 270 |

The electron spectrum of solid insulators | 274 |

Electrons and holes in semiconductors | 277 |

The electron spectrum near the degeneracy point | 279 |

MAGNETISM 69 Equation of motion of the magnetic moment in a ferromagnet | 284 |

Magnons in a ferromagnet The spectrum 20 | 289 |

Magnons in a ferromagnet Thermodynamic quantities | 295 |

The spin Hamihonian | 300 |

Interaction of magnons | 305 |

Magnons in an antiferromagnet | 310 |

ELECTROMAGNETIC FLUCTUATIONS 8 75 Greens function of a photon in a medium | 314 |

Electromagnetic field fluctuations | 319 |

Electromagnetic iluctuations in an infinite medium | 321 |

Current fluctuations in linear circuits | 326 |

Temperature Greens function of a photon in a medium | 327 |

The van der Waals stress tensor | 331 |

Forces of molecular interaction between solid bodies The general formula | 338 |

Forces of molecular interaction between solid bodies Limiting cases | 342 |

Asymptotic behaviour of the correlation function in a liquid | 347 |

Operator expression for the permittivity | 350 |

A degenerate plasma | 353 |

HYDRODYNAMIC FLUCTUATIONS 86 Dynamic form factor of a liquid | 360 |

Summation rules for the form factor | 364 |

Hydrodynamic fluctuations | 368 |

Hydrodynamic fluctuations in an iniinite medium | 373 |

Operator expressions for the transport coefficients | 378 |

Dynamic form factor of a Fermi liquid | 380 |

385 | |

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### Common terms and phrases

atoms Bose liquid calculate chemical potential coefficient commutation condensate condition consider constant coordinates correlation function corresponding crystal definition delta function denotes dependence derivative determined diagram technique distances distribution function electron elementary excitations energy spectrum equation equilibrium expansion expressed in terms external field external lines Fermi gas Fermi liquid Fermi surface ferromagnet finite fluctuations formula Fourier components free energy given gives Green's function half-plane Hamiltonian Heisenberg Hence integrand integration with respect interaction Landau lattice limit linear macroscopic magnetic field magnetic moment magnon matrix elements mean value medium metal momenta motion non-zero number of particles obtain operator pair parameter perturbation theory phase phonon pole problem properties quantum quasi-momentum quasi-particle range replaced result satisfied solution spin Substituting suffix summation superconductivity superfluid symmetry temperature tensor tion transformation transition variable velocity vertex function volume vortex filament wave function zero