## Statistical Physics: Theory of the Condensed StateThe 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 exitations in a quantum Fermi liquid | 1 |

Interaction of quasiparticles | 8 |

Magnetic susceptibility of a Fermi liquid | 12 |

Zero sound | 13 |

Spin waves in a Fermi liquid | 19 |

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

GREENS FUNCTIONS IN A FERMI SYSTEM AT | 28 |

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

The structure of the mixed state | 193 |

Diamagnetic 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 |

Y 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 the vertex function to the quasiparticle interaction function | 68 |

Identities for derivatives of the Greens function | 71 |

Derivation 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 | 88 |

Phonons in a liquid | 94 |

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 apoint | 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 | 124 |

Selfenergy functions | 127 |

Disintegration of quasiparticles | 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 | 159 |

Greens functions in a superfluid Fermi gas | 164 |

Temperature Greens functions in a superfluid Fermi gas | 169 |

Superconductivity in metals | 171 |

44 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 field on electron motion in a lattice | 232 |

Quasiclassical trajectories | 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 | 289 |

Magnons in a ferromagnet Thermodynamic quantities | 294 |

The spin Hamiltonian | 300 |

Interaction of magnons 305 | 305 |

Magnons in an antiferromagnet | 313 |

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

Electromagnetic field fluctuations | 319 |

Electromagnetic fluctuations 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 infinite medium | 373 |

Operator expressions for the transport coefficients | 378 |

Dynamic form factor of a Fermi liquid | 380 |

385 | |

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Statistical Physics: Theory of the Condensed State, Volume 9 E.M. Lifshitz,L. P. Pitaevskii Limited preview - 2013 |

### Common terms and phrases

According applied approximation atoms becomes body Bose calculate closed components condition consider constant contains continuous contribution coordinates correction corresponding crystal defined definition denote density dependence derivative determined diagrams direction distances distribution effect electron energy equal equation excitations expansion expression external fact factor Fermi Fermi surface field fluctuations follows formula Fourier given gives Green's function Hamiltonian Hence independent integral interaction lattice limit lines liquid macroscopic magnetic magnetic field matrix elements means medium metal momentum motion normal obtain occur operators pair particles phase phonon pole potential presence problem properties quantities quantum quasi-particle range regarded relation replaced representation respect result rule satisfied solution spectrum Substituting superconductivity superfluid taken temperature theory thermodynamic tion transformation transition unit variable vector volume vortex wave function written zero