Contents -- Preface -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- 1 Introduction -- I GENERAL THEORY OF OPEN QUANTUM SYSTEMS -- 2 Diverse limited approaches: a brief survey -- 2.1 Langevin equation for a damped classical system -- 2.2 New schemes of quantization -- 2.3 Traditional system-plus-reservoir methods -- 2.3.1 Quantum-mechanical master equations for weak coupling -- 2.3.2 Lindblad theory -- 2.3.3 Operator Langevin equations for weak coupling -- 2.3.4 Generalized quantum Langevin equation -- 2.3.5 Generalized quasiclassical Langevin equation -- 2.3.6 Phenomenological methods -- 2.4 Stochastic dynamics in Hilbert space -- 3 System-plus-reservoir models -- 3.1 Harmonic oscillator bath with linear coupling -- 3.1.1 The Hamiltonian of the global system -- 3.1.2 The road to generalized Langevin equations -- 3.1.3 Phenomenological modeling of friction -- 3.1.4 Quantum statistical properties of the stochastic force -- 3.1.5 Displacement correlation function -- 3.1.6 Thermal propagator and imaginary-time correlations -- 3.1.7 Ohmic and frequency-dependent damping -- 3.1.8 Fractional Langevin equation -- 3.1.9 Rubin model -- 3.1.10 Interaction of a charged particle with the radiation field -- 3.2 Ergodicity -- 3.3 The spin-boson model -- 3.3.1 The model Hamiltonian -- 3.3.2 Flux and charge qubits: reduction to the spin-boson model -- 3.4 Microscopic models -- 3.4.1 Acoustic polaron: one-phonon and two-phonon coupling -- 3.4.2 Optical polaron -- 3.4.3 Interaction with fermions (normal and superconducting) -- 3.4.4 Superconducting tunnel junction -- 3.5 Charging and environmental effects in tunnel junctions -- 3.5.1 The global system for single electron tunneling -- 3.5.2 Resistor, inductor, and transmission lines -- 3.5.3 Charging effects in junctions -- 3.6 Nonlinear quantum environments.

4 Imaginary-time approach and equilibrium dynamics -- 4.1 General concepts -- 4.1.1 Density matrix and reduced density matrix -- 4.1.2 Imaginary-time path integral -- 4.2 Effective action and equilibrium density matrix -- 4.2.1 Open system with bilinear coupling to a harmonic reservoir -- 4.2.2 State-dependent memory friction -- 4.2.3 Spin-boson model -- 4.2.4 Acoustic polaron and defect tunneling: one-phonon coupling -- 4.2.5 Acoustic polaron: two-phonon coupling -- 4.2.6 Tunneling between surfaces: one-phonon coupling -- 4.2.7 Optical polaron -- 4.2.8 Heavy particle in a metal -- 4.2.9 Heavy particle in a superconductor -- 4.2.10 Effective action of a junction -- 4.2.11 Electromagnetic environment -- 4.3 Partition function of the open system -- 4.3.1 General path integral expression -- 4.3.2 Semiclassical approximation -- 4.3.3 Partition function of the damped harmonic oscillator -- 4.3.4 Functional measure in Fourier space -- 4.3.5 Partition function of the damped harmonic oscillator revisited -- 4.4 Quantum statistical expectation values in phase space -- 4.4.1 Generalized Weyl correspondence -- 4.4.2 Generalized Wigner function and expectation values -- 5 Real-time path integrals and nonequilibrium dynamics -- 5.1 Statement of the problem and general concepts -- 5.2 Feynman-Vernon method for a product initial state -- 5.3 Decoherence and friction -- 5.4 General initial states and preparation function -- 5.5 Complex-time path integral for the propagating function -- 5.6 Real-time path integral for the propagating function -- 5.7 Closed time contour representation -- 5.7.1 Complex-time path -- 5.7.2 Real-time path -- 5.8 Semiclassical regime -- 5.8.1 Extremal paths -- 5.8.2 Quasiclassical Langevin equation -- 5.9 Stochastic unraveling of influence functionals -- 5.10 Non-Markovian dissipative dynamics in the semiclassical limit.

5.10.1 Van Vleck and Herman-Kluk propagator -- 5.10.2 Semiclassical dissipative dynamics -- 5.11 Brief summary and outlook -- II MISCELLANEOUS APPLICATIONS -- 6 Damped linear quantum mechanical oscillator -- 6.1 Fluctuation-dissipation theorem -- 6.2 Stochastic modeling -- 6.3 Susceptibility -- 6.3.1 Ohmic friction -- 6.3.2 Ohmic friction with Drude cutoff -- 6.3.3 Radiation damping -- 6.4 The position autocorrelation function -- 6.4.1 Ohmic friction -- 6.4.2 Non-Ohmic spectral density -- 6.4.3 Shiba relation -- 6.5 Partition function and implications -- 6.5.1 Partition function -- 6.5.2 Internal energy, free energy, and entropy -- 6.5.3 Specific heat and Wilson ratio -- 6.5.4 Spectral density of states -- 6.6 Mean square of position and momentum -- 6.6.1 General expressions for colored noise -- 6.6.2 Ohmic friction -- 6.6.3 Ohmic friction with Drude cutoff -- 6.7 Equilibrium density matrix -- 6.7.1 Derivation of the action -- 6.7.2 Purity -- 6.8 Quantum master equations for the reduced density matrix -- 6.8.1 Thermal initial condition -- 6.8.2 Product initial state -- 6.8.3 Approximate time-independent Liouville operators -- 6.8.4 Connection with Lindblad theory -- 7 Quantum Brownian free motion -- 7.1 Spectral density, damping function and mass renormalization -- 7.2 Displacement correlation and response function -- 7.3 Ohmic friction -- 7.3.1 Response function -- 7.3.2 Mean square displacement -- 7.3.3 Momentum spread -- 7.4 Frequency-dependent friction -- 7.4.1 Response function and mobility -- 7.4.2 Mean square displacement -- 7.5 Partition function and thermodynamic properties -- 7.5.1 Partition function -- 7.5.2 Internal and free energy -- 7.5.3 Specific heat -- 7.5.4 Spectral density of states -- 8 The thermodynamic variational approach -- 8.1 Centroid and the effective classical potential -- 8.1.1 Centroid.

8.1.2 The effective classical potential -- 8.2 Variational method -- 8.2.1 Variational method for the free energy -- 8.2.2 Variational method for the effective classical potential -- 8.2.3 Variational perturbation theory -- 8.2.4 Expectation values in coordinate and phase space -- 9 Suppression of quantum coherence -- 9.1 Nondynamical versus dynamical environment -- 9.2 Suppression of transversal and longitudinal interferences -- 9.3 Decoherence in the semiclassical picture -- 9.3.1 A model with localized bath modes -- 9.3.2 Dephasing rate formula -- 9.3.3 Statistical average of paths -- 9.3.4 Ballistic motion -- 9.3.5 Diffusive motion -- 9.4 Decoherence of electrons -- III QUANTUM STATISTICAL DECAY -- 10 Introduction -- 11 Classical rate theory: a brief overview -- 11.1 Classical transition state theory -- 11.2 Moderate-to-strong-damping regime -- 11.3 Strong damping regime -- 11.4 Weak-damping regime -- 12 Quantum rate theory: basic methods -- 12.1 Formal rate expressions in terms of flux operators -- 12.2 Quantum transition state theory -- 12.3 Semiclassical limit -- 12.4 Quantum tunneling regime -- 12.5 Free energy method -- 12.6 Centroid method -- 13 Multidimensional quantum rate theory -- 13.1 The global metastable potential -- 13.2 Periodic orbit and bounce -- 14 Crossover from thermal to quantum decay -- 14.1 Normal mode analysis at the barrier top -- 14.2 Turnover theory for activated rate processes -- 14.3 The crossover temperature -- 15 Thermally activated decay -- 15.1 Rate formula above the crossover regime -- 15.2 Quantum corrections in the pre-exponential factor -- 15.3 The quantum Smoluchowski equation approach -- 15.4 Multidimensional quantum transition state theory -- 16 The crossover region -- 16.1 Beyond steepest descent above T0 -- 16.2 Beyond steepest descent below T0 -- 16.3 The scaling region.

17 Dissipative quantum tunneling -- 17.1 The quantum rate formula -- 17.2 Thermal enhancement of macroscopic quantum tunneling -- 17.3 Quantum decay in a cubic potential for Ohmic friction -- 17.3.1 Bounce action and quantum mechanical prefactor -- 17.3.2 Analytic results for strong Ohmic dissipation -- 17.4 Quantum decay in a tilted cosine potential -- 17.4.1 The case of weak bias -- 17.5 Concluding remarks -- IV THE DISSIPATIVE TWO-STATE SYSTEM -- 18 Introduction -- 18.1 Truncation of the double-well to the two-state system -- 18.1.1 Shifted oscillators and orthogonality catastrophe -- 18.1.2 Adiabatic renormalization -- 18.1.3 Instanton in a double parabolic well -- 18.1.4 Renormalized tunneling matrix element -- 18.1.5 Polaron transformation -- 18.2 Pair interaction in the charge picture -- 18.2.1 Analytic expression for spectral density with any power s -- 18.2.2 Ohmic dissipation and universality limit -- 19 Thermodynamics -- 19.1 Partition function and specific heat -- 19.1.1 Exact formal expression for the partition function -- 19.1.2 Static susceptibility and specific heat -- 19.1.3 The self-energy method -- 19.1.4 The limit of high temperatures -- 19.1.5 Noninteracting-kink-pair approximation -- 19.1.6 Weak-damping limit -- 19.1.7 The self-energy method revisited: partial resummation -- 19.2 Ohmic dissipation -- 19.2.1 Specific heat and Wilson ratio -- 19.2.2 The special case K = 1 2 -- 19.3 Non-Ohmic spectral densities -- 19.3.1 The sub-Ohmic case -- 19.3.2 The super-Ohmic case -- 19.4 Relation between the Ohmic TSS and the Kondo model -- 19.4.1 Anisotropic Kondo model -- 19.4.2 Resonance level model -- 19.5 Equivalence of the Ohmic TSS with the 1/r2 Ising model -- 20 Electron transfer and incoherent tunneling -- 20.1 Electron transfer -- 20.1.1 Adiabatic bath -- 20.1.2 Marcus theory for electron transfer.

20.2 Incoherent tunneling in the nonadiabatic regime.