Projection operators, Hilbert space 143—149
Projection operators, identities of generalized Langevin equations 157—160
Projection operators, initial nonequilibrium states of noise 151—155
Projection operators, linear Langevin equations for slow variables 165—168
Projection operators, matrix form of Liouville equation 144—146
Projection operators, Mori's linear versus exact Langevin equation 160—165
Projection operators, noise in generalized Langevin equations 151—157
Projection operators, non-Markovian fluctuation-dissipation theorem 157
Projection operators, nonlinear to linear example 160—165
Projection operators, partitioning 146—147
Projection operators, projecting 147—148
Projection operators, quantum mechanics 157
Projection operators, subspace of relevant variables 148—149
Projection operators, time correlation functions 158
Quantum Liouville operator, anti-self-adjoint 106
Quantum Liouville operator, Heisenberg representation 105
Quantum Liouville operator, modifications for time-dependent Hamiltonian 105
Quantum Liouville operator, tetradic representation 105
Quantum Liouville operator, time-dependent density matrix 106
Quantum Liouville operator, time-dependent Heisenberg operator 104
Quantum Liouville operator, von Neumann equation 106
Quantum statistical mechanics, energy eigenvalues and eigenfunctions 101—102
Quantum statistical mechanics, equilibrium density matrix 103
Quantum statistical mechanics, Hamiltonian operator 101
Quantum statistical mechanics, quantum Liouville operator 104—106
Quantum statistical mechanics, thermal equilibrium average 103
Quantum statistical mechanics, trace of matrix 103
Quantum statistical mechanics, transformation matrix connecting two sets of states 102—103
Random walks, application of master equations 63—64
Random walks, integral as modified Bessel function 64
Reaction rates, example of ideal gas model system 72—73
Reaction rates, first passage times 74—76
Reaction rates, Kramers problem 76—78
Reaction rates, Kramers problem and energy diffusion 78—82
Reaction rates, transition state theory 67—72
Recurrence paradox, example of one-dimensional harmonic lattice 195—196
Recurrence paradox, objection to Boltzmann's H-theorem 194
Recurrence paradox, recurrence time 196
Reversibility paradox, example of one-dimensional harmonic lattice 195
Reversibility paradox, objection to Boltzmann's H-theorem 193—194
Reversibility paradox, one-way irreversible character appearing to violate time-reversal symmetry 193—194
Rotational diffusion, derivation of equation 84—88
Rotational diffusion, evaluating continued fractions by truncation 88
Rotational diffusion, kinetic model 84—88
Shear viscosity, coefficient 99
Shear viscosity, deriving formula 99
Shear viscosity, ratio to thermal conductivity 100
Shear viscosity, time correlation function determining 168
Slow variables, diffusion coefficient 182 186—187
Slow variables, equilibrium distribution 185—187
Slow variables, Fokker — Planck equation 183
Slow variables, Langevin equation 183
Slow variables, streaming velocity, Langevin equation 185—186
Smoluchowski equation, first passage times 75
Smoluchowski equation, Fokker — Planck equation 40—41
Smoluchowski equation, substitution leading to Schrodinger-like equation 41
Spectral density, absorption coefficient proportional to, of dipole-dipole time correlation function 12
Spectral density, correlation function 139
Spectral density, Fourier transform of time correlation function 8
Spin-boson Hamiltonian, electron transfer kinetics 108
Static linear response, determining equilibrium 127—129
Static linear response, electric dipole moment 128
Static linear response, Kubo transform 129—130
Static linear response, quantum mechanical version 129—130
Static linear response, quantum perturbation theory 130
Static linear response, unperturbed and perturbed distribution function 128
Static linear response, unperturbed and perturbed partition function 128
Stokes — Einstein formula, friction coefficient 12
Stress tensor, hydrodynamics 97
Stress tensor, Navier — Stokes form of viscous 99
| Stress time correlation function, deriving long tail time 173
Stress time correlation function, long time tails 170
Superoperator, quantum commutator 104
Taylor's series expansion, time-dependent dynamical variable 34
Thermal conductivity, deriving formula 99—100
Thermal conductivity, Fourier's heat law 100
Thermal conductivity, heat current 99—100
Thermal conductivity, mode-coupling theory 169
Thermal conductivity, ratio to viscosity 100
Time correlation functions, combining Bloch equations 120
Time correlation functions, derivation for orientational 89—92
Time correlation functions, determining properties of systems out of equilibrium 7
Time correlation functions, dipole-dipole correlation function 12—14
Time correlation functions, equilibrium fluctuations in particle number 15
Time correlation functions, fluctuating magnetic field 60
Time correlation functions, fluctuation, nonlinear for slow variables 184
Time correlation functions, frequency dependence of optical absorption coefficient 53
Time correlation functions, generalized Langevin equations 158
Time correlation functions, integral over angular velocities only 89
Time correlation functions, Langevin equation 7—10
Time correlation functions, Liouville operator notation 35—36
Time correlation functions, mean squared displacement 11—12
Time correlation functions, orientational, of planar Brownian rotator 45—47
Time correlation functions, spectral density 8
Time correlation functions, statistical behavior of time-dependent quantity 7—8
Time correlation functions, Stehfest algorithm 92
Time correlation functions, transition state theory 72
Time correlation functions, two-level system in heat bath 118—119
Time correlation functions, using partition functions 8
Time correlation functions, velocity correlation function 8—11
Time derivative, Laplace transforms 203
Transition state theory, alternative form using quantum mechanical partition function 70—72
Transition state theory, approximation 68
Transition state theory, escape rate 73
Transition state theory, example of ideal gas escape from two-dimensional region 72—73
Transition state theory, flux density 68
Transition state theory, Hamiltonian 68—69
Transition state theory, model system 73f
Transition state theory, partition function of transition state 70—71
Transition state theory, phase space distribution function 67
Transition state theory, probability of being in region 68
Transition state theory, rate constant 69—70
Transition state theory, rate constant as ratio of two partition functions 70
Transition state theory, rate equations 69—70
Transition state theory, rates of chemical reactions 67
Transition state theory, relation of Kramers rate to, rate 78
Transition state theory, time correlation function 72
Transition state theory, transitions between regions by simple first-order kinetics 71
Transport equations, diffusion equation 207
Transport equations, hydrodynamic equations 207—208
Transport equations, phenomenological 207—209
Two-level system, approximate methods 113—115
Two-level system, caution for Markovian approximations 115
Two-level system, density matrix 110—111
Two-level system, dipole time correlation function 111—112
Two-level system, equation of motion for density matrix 111
Two-level system, exact solution procedure 112—113
Two-level system, heat bath, Bloch equations 115—121
Two-level system, heat bath, dephasing 110—115
Two-level system, spectral line shape by dipole-dipole line correlation function 111
Velocity correlation function, Brownian particle 10—11
Velocity correlation function, connection with self-diffusion coefficient 8—10
Velocity correlation function, fluctuation-dissipation theorem 11
Velocity correlation function, heavy mass in harmonic lattice 24—28
Velocity correlation function, Hilbert space expansion 171
Velocity correlation function, ion mobility 137
Velocity correlation function, long time tails 169—170
Velocity correlation function, mode-coupling theory 171—173
Velocity correlation function, random behavior at long times 196f
von Neumann equation, quantum Liouville equation 106
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