ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Statistical Physics

:	Michael V. Sadovskii
:	Statistical Physics
:	Walter de Gruyter GmbH& Co.KG
:	9783110270372
:	De Gruyter Studies in Mathematical PhysicsISSN
:	1
:	CHF 169.40
:

:	Theoretische Physik
:	English

:	292
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

< PAN lang=EN>

This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.

< >Michael V. Sadovskii, Institute for Electrophysics, Russian Academy of Sciences, Russia.

	Preface	5
	1 Basic principles of statistics	11
	1.1 Introduction	12
	1.2 Distribution functions	12
	1.3 Statistical independence	17
	1.4 Liouville theorem	19
	1.5 Role of energy, microcanonical distribution	23
	1.6 Partial distribution functions	27
	1.7 Density matrix	31
	1.7.1 Pure ensemble	32
	1.7.2 Mixed ensemble	34
	1.8 Quantum Liouville equation	36
	1.9 Microcanonical distribution in quantum statistics	38
	1.10 Partial density matrices	39
	1.11 Entropy	42
	1.11.1 Gibbs entropy. Entropy and probability	42
	1.11.2 The law of entropy growth	45
	2 Gibbs distribution	53
	2.1 Canonical distribution	53
	2.2 Maxwell distribution	58
	2.3 Free energy from Gibbs distribution	60
	2.4 Gibbs distribution for systems with varying number of particles	62
	2.5 Thermodynamic relations from Gibbs distribution	65
	3 Classical ideal gas	70
	3.1 Boltzmann distribution	70
	3.2 Boltzmann distribution and classical statistics	71
	3.3 Nonequilibrium ideal gas	73
	3.4 Free energy of Boltzmann gas	76
	3.5 Equation of state of Boltzmann gas	77
	3.6 Ideal gas with constant specific heat	79
	3.7 Equipartition theorem	80
	3.8 One-atom ideal gas	82
	4 Quantum ideal gases	85
	4.1 Fermi distribution	85
	4.2 Bose distribution	86
	4.3 Nonequilibrium Fermi and Bose gases	87
	4.4 General properties of Fermi and Bose gases	89
	4.5 Degenerate gas of electrons	92
	4.6 Relativistic degenerate electron gas	95
	4.7 Specific heat of a degenerate electron gas	96
	4.8 Magnetism of an electron gas in weak fields	98
	4.9 Magnetism of an electron gas in high fields	102
	4.10 Degenerate Bose gas	104
	4.11 Statistics of photons	107
	5 Condensed matter	111
	5.1 Solid state at low temperature	111
	5.2 Solid state at high temperature	114
	5.3 Debye theory	115
	5.4 Quantum Bose liquid	119
	5.5 Superfluidity	123
	5.6 Phonons in a Bose liquid	127
	5.7 Degenerate interacting Bose gas	131
	5.8 Fermi liquids	134
	5.9 Electron liquid in metals	140
	6 Superconductivity	143
	6.1 Cooper instability	143
	6.2 Energy spectrum of superconductors	145
	6.3 Thermodynamics of superconductors	154
	6.4 Coulomb repulsion	158
	6.5 Ginzburg-Landau theory	161
	7 Fluctuations	170
	7.1 Gaussian distribution	170
	7.2 Fluctuations in basic physical properties	174
	7.3 Fluctuations in ideal gases	177
	8 Phase transitions and critical phenomena	180
	8.1 Mean-field theory of magnetism	180
	8.2 Quasi-averages	187
	8.3 Fluctuations in the order parameter	190
	8.4 Scaling	196
	9 Linear response	205
	9.1 Linear response to mechanical perturbation	205
	9.2 Electrical conductivity and magnetic susceptibility	211
	9.3 Dispersion relations	214
	10 Kinetic equations	218
	10.1 Boltzmann equation	218
	10.2 H-theorem	224
	10.3 Quantum kinetic equations	226
	10.3.1 Electron-phonon interaction	228
	10.3.2 Electron-electron interaction	232
	11 Basics of the modern theory of many-particle systems	235
	11.1 Quasiparticles and Green's functions	235
	11.2 Feynman diagrams for many-particle systems	243
	11.3 Dyson equation	247
	11.4 Effective interaction and dielectric screening	251
	11.5 Green’s functions at finite temperatures	254
	A Motion in phase space, ergodicity and mixing	258
	A.1 Ergodicity	258
	A.2 Poincare recurrence theorem	264
	A.3 Instability of trajectories and mixing	266
	B Statistical mechanics and information theory	269
	B.1 Relation between Gibbs distributions and the principle of maximal information entropy	269
	B.2 Purging Maxwell's “demon”	273
	C Nonequilibrium statistical operators	280
	C.1 Quasi-equilibrium statistical operators	280
	C.2 Nonequilibrium statistical operators and quasi-averages	283
	Bibliography	287
	Index	289