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| Dalvit D.A.R., Frastai J., Lawrie I.D. — Problems on statistical mechanics |
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| Предметный указатель |
Antiferromagnet 5.16 5.22
Antiparticles 4.26
Atmosphere, idealized model of Earth’s 6.19
Black — Scholes equation 6.4
Black-body radiation 9 2.11 4.4 4.5
Boltzmann counting 6 3.1 4.2
Boltzmann equation 14 6.17
Boltzmann equation for fermions 6.21
Boltzmann equation, relaxation time approximation 15 6.17 6.18 6.22—6.24
Bose — Einstein condensation 4.12 4.14 4.15
Bose — Einstein gas 4.12—4.15
Bose — Einstein statistics 9 4.1—4.3
Boyle temperature 5.3
Brillouin function 5.26
Brownian motion 16 6.12
Brownian motion, geometric, of stock prices 6.3
canonical ensemble 6 3.9—3.22 3.28—3.30
chemical potential 2 4 7 3.23 3.24 4.22
Chemical potential and Fermi energy 4.17 4.18 4.26
Classical gas 3.1 3.2
Classical gas with absorbing walls 3.25 3.26
Classical gas, relativistic 3.3
Classical gas, specific heats 2.9 3.3 3.20
Classical gas, transport processes 6.17—6.20
Clausius — Clapeyron equation 4.12
Compressibility, adiabatic 5 2.4
Compressibility, isothermal 5 2.4.
Compressibility, isothermal, divergence at critical point 4.13 5.8.
Compressibility, isothermal, of Fermi — Dirac gas 4.17
Conduction, thermal 6.14 6.15 6.20
Conductivity, electrical, charged gas 6.13
Conductivity, electrical, Drude’s theory 6.13
Conductivity, electrical, metals 6.13 6.22 6.24
Conductivity, electrical, metals, frequency-dependent 6.23
Correlation function 5.14 5.16 5.20 5.21
correlation length 5.16 5.28
Critical exponents 13
Critical exponents and amplitude ratios, universality of 5.23
Critical exponents for Heisenberg model in mean-field approximation 5.23
Critical exponents for Ising model in mean-field approximation 5.24
Critical exponents for van-der-Waals gas 5.8
Critical exponents from renormalization group 5.28
Critical isochore 5.9
Critical isotherm 5.8 5.9
Critical point 13 5.8 5.9 5.23—5.26 5.28
Critical point, scaling 5.8 5.9 5.28
Critical temperature 13
Cumulant average 3.13
Curie temperature 13
Curie — Weiss law 5.22
Curie’s law 3.14 4.23
Debye temperature 4.10
Debye’s approximation 4.8—4.11
Density matrix 6.21
Density of states 10 4.2 4.6 4.12
Detailed balance 4.5
Diatomic gas 3.18 3.19 3.21
Diffusion of heat 15 6.14 6.15
Diffusion of particles 15 6 6.2 6.4 6.7 6.12 6.13 6.17
Dirac sea 4.26
Distinguishable and indistinguishable particles 6 9 3.4 4.1 4.2
Distribution function 14 6.10 6.11 6.17—6.19
Distribution function, Wigner 6.21—6.24
Domain wall 6.16
Early Universe 2.11
Ensemble, Canonical 6 3.8—3.22
Ensemble, Grand Canonical 6 3.23—3.26
Ensemble, isobaric 7 3.27
Ensemble, microcanonical 5 3.1—3.8
Ensemble, relationships between microcanonical, canonical and grand canonical 3.2 3.8 3.28—3.30
Entropy and information 2 2.3 3.6 3.8
Entropy, extensivity of 4 3.4
Equipartition of energy 3.4 3.10 3.18 3.20 3.27 4.11 6.12
Euler — Maclaurin formula 3.18
Euler’s equation 4
Extensive variables 4
Fermi energy 11 4.17 4.18
Fermi sea 4.26
Fermi temperature 4.17
Fermi — Dirac gas 4.17—4.29
Ferromagnet 12 5.17 5.22—5.26
First law of thermodynamics 2 3 2.8 2.10
Fluctuation-dissipation relation 6.12 6.13
Fluctuations 7
Fluctuations in energy and particle number 3.28 4.2 4.3
Fokker — Planck equation 6
Free energy, Gibbs 3 7 2.1 2.10 4.13 5.8 5.9
Free energy, Helmholtz 3 6 2.1 3.6 3.8 3.13 3.29 4.13 5.1 5.2
Free energy, Landau 5.8
Frustration 5.16
Fugacity 7 3.25 4.2 4.12 4.15 4.25
Gibbs free energy 3 7 2.1 2.10
Gibbs free energy of Bose gas 4.13
Gibbs free energy of van-der-Waals gas 5.8
Gibbs free energy, scaling near a critical point 5.9
Gibbs — Duhem equation 4 2.5
Ginzburg — Landau equation, time-dependent 6.16
grand canonical ensemble 6 3.23—3.26
Grand canonical ensemble, fluctuations of particle number and energy 3.28
Grand canonical ensemble, relationship with other ensembles 3.28—3.30
Grand potential 3 7 3.25 3.28
Hall coefficient 6.22
Harmonic forces, chain of particles bound by 4.7 4.11
Harmonic oscillators 3.4 3.5 3.9 4.7
Heisenberg model 5.19 5.23
Helmholtz free energy 3 6 2.1 3.6 3.8 3.13 3.29 4.13
Helmholtz free energy of non-ideal gas 5.1 5.2
Holes 4.26
Hubbard — Stratonovich transformation 5.17
Ideal classical gas 2.7 3.1 3.25 3.26
Ideal quantum gas 3.2
Ideal quantum gas, Bose — Einstein 4.12—4.15
| Ideal quantum gas, Fermi — Dirac 4.17—1.29
Indistinguishable and distinguishable particles 6 9 3.4 4.1 4.2
Information and entropy 2 2.3 3.6 3.8
Intensive variables 4
Internal energy 2 3.13
Internal energyand pressure of an ideal gas 10 4.21
Internal energyand pressure of imperfect gas 5.1 5.2 5.4
Internal energyof 2-dimensional gas 3.12
Internal energyof a long elastic molecule 3.27
Internal energyof diatomic gas 3.19 3.22
Inversion temperature, Joule — Kelvin 5.3
Ising model 12 5.13 5.14 5.16—5.18 5.20—5.22 5.24—5.26 5.28
Ising model and lattice gas 5.12
Isobaric ensemble 7 3.27
Joule effect 2.8
Joule — Kelvin process 5.3
Landau free energy 5.8
Landau levels 4.23
Langevin equation 16 6.12 6.13
Langevin function 3.14 3.15
Lattice gas 3.16 3.24
Lattice gas and Ising model 5.12
Magnetic material, thermodynamic properties of 2.10
magnetic susceptibility 13
Magnetic susceptibility of antiferromagnet 5.22
Magnetic susceptibility, critical behaviour 13 5.23 5.24
Magnetic susceptibility, relation to correlation function 5.20
magnetization 13 2.10
Magnetization, critical behaviour 5.23 5.24
Magnetization, paramagnet 3.14
Magnetization, spontaneous 13
Magnetization, staggered (or sublattice) 5.22
Markov process (or chain) 15 6.5 6.6
Master equation 16 6
Maxwell equal-areas construction 5.8
Maxwell relations 3 2.4 2.5 2.8—2.10
Maxwell — Boltzmann statistics 9 4.1—4.3 4.21
Mean-field approximation 13 5.22—5.26
microcanonical ensemble 5 3.1—3.8
Morse potential 3.22
Negative temperature 2.2 3.6—3.8
Neutrinos 2.11
Nuclear shell model 5.10
Ordering field 5.22
Pair potential 5.1 5.3—5.5 5.7
Partition function canonical 6 3.9—3.22
Partition function grand canonical 7 3.23—3.26
Phase transition 13 (see also “Critical point”)
Phase transition in Bose — Einstein gas 4.12—4.14
Phase transition, Landau theory 5.8 6.16
Phonons 9 4.7—4.11
Phonons, optical and acoustic branches of spectrum 4.11
Potentials, thermodynamic 3 2.7 2.10
Potentials, thermodynamic, associated with statistical ensembles 6—8
Potts model 5.11
Random walk 6.1—6.4
Random walk, stock prices 6.3 6.4
Relativistic gases 2.11 3.3 3.23 4.4. 4.26 4.27
Relaxation-time approximation 15 6.17 6.18 6
Renormalization group 5.28
Rotons 4.16
Saddle-point approximation 5.17
Scaling 5.8 5.9 5.28
Second law of thermodynamics 2 2.1 2.2
Soliton 6.16
Specific heat (or heat capacity) 4 3.10 3.11
Specific heat (or heat capacity) of black body radiation 4.4
Specific heat (or heat capacity) of diatomic and polyatomic gases 3.18 3.20 3.21
Specific heat (or heat capacity) of superfluid 4.16
Specific heat (or heat capacity) of van-der-Waals gas 2.9
Specific heat (or heat capacity), Bose — Einstein gas 4.12
Specific heat (or heat capacity), critical behaviour 4.12 5.9 5.24
Specific heat (or heat capacity), phonon contribution 4.7—4.11
Specific heat (or heat capacity), principal 4 2.4 2.8
Specific heat (or heat capacity), principal, ratio 3.3
Staggered magnetic field 5.22
Statistics, Bose — Einstein 9 4.1—4.3
Statistics, Fermi — Dirac 9 4.1—4.3
Statistics, Maxwell — Boltzmann 9 4.1—4.3 4.21
Stefan — Boltzmann constant 4.4
Superfluid 4.16
Susceptibility, diamagnetic 4.23
Susceptibility, magnetic 13
Susceptibility, magnetic of antiferromagnet 5.22
Susceptibility, magnetic, critical behaviour 13 5 5.24
Susceptibility, magnetic, relation to correlation function 5.20
Susceptibility, paramagnetic 4
Temperature in microcanonical ensemble 3.1 3.6
Temperature, absolute thermodynamic scale 2
Temperature, negative 2.2 3.6—3.8
Thermal conductivity of a gas 6.17—6.20
Thermal conductivity of a metal 6.22 6.24
Thermal de Broglie wavelength 12 3.18
Thermal expansivity 2.4
Thermodynamic limit 3.2 3.5 3.6 3.30 4.12 5.2 5.11
Thermodynamic potentials 3 2.7 2.10
Thermodynamic potentials, associated with statistical ensembles 6—8
Thermodynamics, first law of 2 3 2.8 2.10
Thermodynamics, fundamental equation of 4
Thermodynamics, second law of 2 2.1 2.2
Thermodynamics, third law of 2 3.11 3.18
Thermoelectric power 6.22. 6
Time-dependent Ginzburg — Landau equation 6.16
Transfer matrix 5.11 5.13 5.14 5.16
van Leeuwen’s theorem 4.23
van-der-Waals gas 2.9
van-der-Waals gas, critical properties 5.8
Virial expansion 5.2—5.7
Virial expansion for a mixture of two gases and 5.7
Virial expansion for hard-sphere gas 5.6
viscosity 6.17
Wigner distribution function 6.21—6.24
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