| Introduction |
|
9 | (12) |
| Frequently used formulae |
|
18 | (2) |
| Errata to Volume 1 |
|
20 | (1) |
|
5 Linear irreversible processes |
|
|
21 | (84) |
|
5.1 Linear response to mechanical perturbations |
|
|
22 | (23) |
|
|
|
22 | (6) |
|
5.1.2 Equilibrium correlation functions and retarded Green's functions |
|
|
28 | (4) |
|
5.1.3 The response to stationary perturbations |
|
|
32 | (1) |
|
5.1.4 Kubo's approach to linear response theory |
|
|
33 | (3) |
|
5.1.5 Isolated and isothermal susceptibility |
|
|
36 | (4) |
|
5.1.6 Magnetic susceptibility |
|
|
40 | (2) |
|
5.1.7 Electrical conductivity |
|
|
42 | (3) |
|
5.2 Properties of susceptibilities and kinetic coefficients |
|
|
45 | (14) |
|
5.2.1 The spectral density |
|
|
46 | (1) |
|
|
|
47 | (5) |
|
5.2.3 Onsager's reciprocity relations |
|
|
52 | (2) |
|
5.2.4 Dispersion relations |
|
|
54 | (1) |
|
|
|
55 | (2) |
|
5.2.6 Fluctuation-dissipation theorems |
|
|
57 | (2) |
|
5.3 The memory function formalism |
|
|
59 | (16) |
|
5.3.1 Linear evolution equations for observables |
|
|
60 | (5) |
|
5.3.2 Macroscopic dynamics of magnetic systems |
|
|
65 | (3) |
|
5.3.3 Connection between memory functions and correlation functions |
|
|
68 | (3) |
|
5.3.4 Relaxation time and the "plateau problem" |
|
|
71 | (4) |
|
5.4 Linear transport processes |
|
|
75 | (10) |
|
5.4.1 Linear kinetic equations |
|
|
75 | (4) |
|
5.4.2 Linear hydrodynamic equations |
|
|
79 | (3) |
|
|
|
82 | (3) |
|
|
|
85 | (17) |
|
5A Variational principle in linear response theory |
|
|
85 | (5) |
|
5B Isothermal and adiabatic electrical conductivity |
|
|
90 | (5) |
|
5C Linear response to thermal perturbations: thermoelectric transport coefficients |
|
|
95 | (5) |
|
5D Mori's representation of correlation functions |
|
|
100 | (2) |
|
|
|
102 | (3) |
|
6 Nonequilibrium correlations and Green's functions |
|
|
105 | (68) |
|
6.1 Nonequilibrium thermodynamic correlations |
|
|
106 | (19) |
|
6.1.1 Perturbation expansion of nonequilibrium equations of state |
|
|
107 | (3) |
|
6.1.2 Nonequilibrium thermodynamic Green's functions |
|
|
110 | (4) |
|
6.1.3 Perturbation expansion of thermodynamic Green's functions |
|
|
114 | (2) |
|
6.1.4 Thermodynamic Green's functions for Fermi and Bose systems |
|
|
116 | (2) |
|
6.1.5 Nonequilibrium correlations in an electron gas |
|
|
118 | (7) |
|
6.2 Correlations in quasi-equilibrium states |
|
|
125 | (13) |
|
6.2.1 Thermodynamic Green's functions in quasi-equilibrium |
|
|
126 | (3) |
|
6.2.2 Generalized susceptibility in the Green's function formalism |
|
|
129 | (1) |
|
6.2.3 The dielectric function for a charged particle system |
|
|
130 | (3) |
|
6.2.4 Kinetic coefficients in the Green's function formalism |
|
|
133 | (2) |
|
6.2.5 The electrical conductivity of high-temperature plasmas |
|
|
135 | (3) |
|
6.3 Nonequilibrium real-time Green's functions |
|
|
138 | (25) |
|
6.3.1 The definition of real-time Green's functions |
|
|
138 | (2) |
|
6.3.2 Equations of motion and the Dyson equation |
|
|
140 | (4) |
|
6.3.3 The generalized kinetic equation |
|
|
144 | (3) |
|
6.3.4 The quasiparticle approximation |
|
|
147 | (7) |
|
6.3.5 Boundary conditions for the real-time Green's functions |
|
|
154 | (2) |
|
6.3.6 Inclusion of thermodynamic correlations |
|
|
156 | (7) |
|
|
|
163 | (5) |
|
6A Evaluation of sums over discrete frequencies |
|
|
163 | (1) |
|
6B Approximate dielectric function |
|
|
164 | (3) |
|
6C The gradient expansion in the generalized kinetic equation |
|
|
167 | (1) |
|
|
|
168 | (5) |
|
7 Nonlinear relaxation processes |
|
|
173 | (64) |
|
7.1 Weakly interacting subsystems |
|
|
173 | (16) |
|
7.1.1 Energy exchange between two subsystems |
|
|
174 | (4) |
|
7.1.2 The kinetic coefficient for energy exchange |
|
|
178 | (3) |
|
7.1.3 Particle and energy exchange between subsystems |
|
|
181 | (3) |
|
7.1.4 Hot-electron transport in semiconductors |
|
|
184 | (5) |
|
|
|
189 | (14) |
|
7.2.1 The generalized master equation |
|
|
190 | (3) |
|
7.2.2 Perturbation expansion of the master equation |
|
|
193 | (2) |
|
7.2.3 Master equation for the electron-impurity system |
|
|
195 | (5) |
|
7.2.4 Master equation for classical fluids |
|
|
200 | (3) |
|
7.3 Relaxation processes in open systems |
|
|
203 | (10) |
|
7.3.1 The master equation for a system in a heat bath |
|
|
203 | (3) |
|
7.3.2 The master equation in the Born approximation |
|
|
206 | (1) |
|
7.3.3 Example: a quantum oscillator in a heat bath |
|
|
207 | (3) |
|
7.3.4 The quantum Fokker-Planck equation |
|
|
210 | (3) |
|
7.4 Kinetic processes in lasers |
|
|
213 | (10) |
|
7.4.1 A single-mode laser with two-level active atoms |
|
|
213 | (3) |
|
7.4.2 The master equation for the field-atom subsystem |
|
|
216 | (3) |
|
|
|
219 | (2) |
|
7.4.4 Atomic correlations in a laser |
|
|
221 | (2) |
|
|
|
223 | (11) |
|
7A The entropy production operator for hot-electron transport |
|
|
223 | (2) |
|
7B The coherent-state representation |
|
|
225 | (2) |
|
7C Quantum operators in the coherent-state representation |
|
|
227 | (7) |
|
|
|
234 | (3) |
|
|
|
237 | (63) |
|
8.1 A general theory of hydrodynamic processes |
|
|
237 | (5) |
|
8.1.1 Local conservation laws |
|
|
237 | (1) |
|
8.1.2 Generalized hydrodynamic equations |
|
|
238 | (2) |
|
8.1.3 Markovian and local approximations |
|
|
240 | (2) |
|
8.2 Transport processes in a one-component fluid |
|
|
242 | (17) |
|
8.2.1 Local conservation laws |
|
|
242 | (3) |
|
8.2.2 The ideal fluid hydrodynamics |
|
|
245 | (4) |
|
8.2.3 The local kinetic coefficients |
|
|
249 | (4) |
|
8.2.4 Transport coefficients |
|
|
253 | (3) |
|
8.2.5 Dissipative processes in a one-component fluid |
|
|
256 | (3) |
|
8.3 A multicomponent fluid |
|
|
259 | (10) |
|
8.3.1 Local equilibrium in a multicomponent fluid |
|
|
259 | (2) |
|
8.3.2 Transport equations |
|
|
261 | (5) |
|
8.3.3 Transport processes in a binary mixture |
|
|
266 | (3) |
|
8.4 Superfluid hydrodynamics |
|
|
269 | (22) |
|
8.4.1 The equilibrium state of a Bose superfluid |
|
|
269 | (4) |
|
8.4.2 The local-equilibrium distribution for a superfluid |
|
|
273 | (2) |
|
8.4.3 Local thermodynamic relations for a superfluid |
|
|
275 | (4) |
|
8.4.4 Hydrodynamic equations for an ideal superfluid |
|
|
279 | (5) |
|
8.4.5 Dissipative processes in superfluid hydrodynamics |
|
|
284 | (7) |
|
|
|
291 | (7) |
|
8A Local thermodynamic relations for classical fluids |
|
|
291 | (2) |
|
8B Transformation of phase variables in hydrodynamics |
|
|
293 | (3) |
|
8C The entropy production operator for a superfluid |
|
|
296 | (2) |
|
|
|
298 | (2) |
|
9 Hydrodynamic fluctuations |
|
|
300 | (63) |
|
9.1 Time evolution of large-scale fluctuations |
|
|
300 | (16) |
|
9.1.1 Distribution function of hydrodynamic variables |
|
|
301 | (2) |
|
9.1.2 The generalized Fokker-Planck equation |
|
|
303 | (4) |
|
9.1.3 The gradient expansion in the Fokker-Planck equation |
|
|
307 | (3) |
|
9.1.4 Functional form of the Fokker-Planck equation |
|
|
310 | (3) |
|
9.1.5 The entropy functional for hydrodynamic fluctuations |
|
|
313 | (3) |
|
9.2 Fluctuations in a one-component fluid |
|
|
316 | (10) |
|
9.2.1 Thermodynamics of fluctuations |
|
|
316 | (2) |
|
9.2.2 The drift terms and the bare kinetic coefficients |
|
|
318 | (3) |
|
9.2.3 The Langevin formalism in fluctuating hydrodynamics |
|
|
321 | (5) |
|
9.3 Hydrodynamic fluctuations in nonequilibrium steady states |
|
|
326 | (14) |
|
9.3.1 Time correlations of the nonequilibrium fluctuations |
|
|
327 | (3) |
|
9.3.2 The linearized Langevin equations for a simple fluid |
|
|
330 | (1) |
|
9.3.3 Density fluctuations in steady states: sound frequencies |
|
|
331 | (6) |
|
9.3.4 Density fluctuations in steady states: low frequencies |
|
|
337 | (3) |
|
9.4 Statistical mechanics of turbulence |
|
|
340 | (14) |
|
9.4.1 Statistical description of turbulent flows in fluids |
|
|
340 | (2) |
|
9.4.2 The Fokker-Planck equation for turbulent flows |
|
|
342 | (3) |
|
9.4.3 Separation of variables in the Fokker-Planck equation |
|
|
345 | (1) |
|
9.4.4 The Reynolds equations |
|
|
346 | (2) |
|
9.4.5 The entropy and the free energy of turbulent flow |
|
|
348 | (3) |
|
9.4.6 Normal solutions of the Fokker-Planck equation |
|
|
351 | (3) |
|
|
|
354 | (7) |
|
9A The projection operator in fluctuating hydrodynamics |
|
|
354 | (2) |
|
9B The equilibrium solution of the Fokker-Planck equation |
|
|
356 | (1) |
|
9C Derivation of the Fokker-Planck equation from stochastic hydrodynamic equations |
|
|
357 | (4) |
|
|
|
361 | (2) |
| Conclusion |
|
363 | (3) |
| Bibliography |
|
366 | (7) |
| Index |
|
373 | |
