Contents -- Preface -- Preface to the Second Edition -- Acknowledgements -- 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 Operator Langevin equations for weak coupling -- 2.3.3 Quantum and quasiclassical Langevin equation -- 2.3.4 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 the classical generalized Langevin equation -- 3.1.3 Phenomenological modeling -- 3.1.4 Quasiclassical Langevin equation -- 3.1.5 Ohmic and frequency-dependent damping -- 3.1.6 Rubin model -- 3.2 The Spin-Boson model -- 3.2.1 The model Hamiltonian -- 3.2.2 Josephson two-state systems: flux and charge qubit -- 3.3 Microscopic models -- 3.3.1 Acoustic polaron: one-phonon and two-phonon coupling -- 3.3.2 Optical polaron -- 3.3.3 Interaction with fermions (normal and superconducting) -- 3.3.4 Superconducting tunnel junction -- 3.4 Charging and environmental effects in tunnel junctions -- 3.4.1 The global system €or single electron tunneling -- 3.4.2 Resistor, inductor and transmission lines -- 3.4.3 Charging effects in Josephson junctions -- 3.5 Nonlinear quantum environments -- 4 Imaginary-time path integrals -- 4.1 The density matrix: general concepts -- 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 for a Josephson 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 -- 4.4Quantum 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 dynamics -- 5.1 Feynman-Vernon method for a product initial state -- 5.2 Decoherence and friction -- 5.3 General initial states and preparation function -- 5.4 Complex-time path integral for the propagating function -- 5 5 Real-time path integral for the propagating function -- 5.5.1 Extremal paths -- 5.5.2 Classical limit -- 5.5.3 Semiclassical limit: quasiclassical Langevin equation -- 5.6 Stochastic unraveling of influence functionals -- 5.7 Brief summary and outlook -- II FEW SIMPLE APPLICATIONS -- 6 Damped harmonic oscillator -- 6.1 Fluctuation-dissipation theorem -- 6.2 Stochastic modeling -- 6.3 Susceptibility for Ohmic friction and Drude damping -- 6.3.1 Strict Ohmic friction -- 6.3.2 Drude damping -- 6.4 The position autocorrelation function -- 6.4.1 Ohmic damping -- 6.4.2 Algebraic spectral density -- 6.5 Partition function, internal energy and density of states -- 6.5.1 Partition function and internal energy -- 6.5.2 Spectral density of states -- 6.6 Mean square of position and momentum -- 6.6.1 General expressions for coloured noise -- 6.6.2 Strict Ohmic case.

6.6.3 Ohmic friction with Drude regularization -- 6.7 Equilibrium density matrix -- 6.7.1 Purity -- 7 Quantum Brownian free motion -- 7.1 Spectral density. damping function and mass renormalization -- 7.2 Displacement correlation and response function -- 7.3 Ohmicdamping -- 7.4 Frequency-dependent damping -- 7.4.1 Response function and mobility -- 7.4.2 Mean square displacement -- 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 Localized bath modes and universal decoherence -- 9.3.1 A model with localized bath modes -- 9.3.2 Statistical average of paths -- 9.3.3 Ballistic motion -- 9.3.4 Diffusive motion -- 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 -- 1 2 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 -- 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 preexponential 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 To -- 16.2 Beyond steepest descent below To -- 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 prefactor -- 17.3.2 Analytic results for strong Ohmic dissipation -- 17.4 Quantum decay in a tilted cosine washboard potential -- 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 Renormalized tunnel matrix element -- 18.1.4 Polaron transformation -- 18.2 Pair interaction in the charge picture -- 18.2.1 Analytic expression for any s and arbitrary cutoff w, -- 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 General results -- 19.2.2 The special case K = f -- 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 l/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 -- 20.2.1 General expressions for the nonadiabatic rate -- 20.2.2 Probability for energy exchange: general results -- 20.2.3 The spectral probability density for absorption at T = 0 -- 20.2.4 Crossover from quantum-mechanical to classical behaviour -- 20.2.5 The Ohmic case -- 20.2.6 Exact nonadiabatic rates for K = l / 2 and K = 1 -- 20.2.7 The sub-ohmic case (0 1) -- 20.2.9 Incoherent defect tunneling in metals -- 20.3 Single charge tunneling -- 20.3.1 Weak-tunneling regime -- 20.3.2 The current-voltage characteristics -- 20.3.3 Weak tunneling of 1D interacting electrons -- 20.3.4 Tunneling of Cooper pairs -- 20.3.5 Tunneling of quasiparticles -- 21 Two-state dynamics -- 21.1 Initial preparation, expectation values, and correlations -- 21.1.1 Product initial state -- 21.1.2 Thermal initial state -- 21.2 Exact formal expressions for the system dynamics -- 21.2.1 Sojourns and blips -- 21.2.2 Conditional propagating functions -- 21.2.3 The expectation values (0, ) t ( j = z, y, z ) -- 21.2.4 Correlation and response function of the populations -- 21.2.5 Correlation and response function of the coherences -- 21.2.6 Generalized exact master equation and integral relations -- 21.3 The noninteracting-blip approximation (NIBA) -- 21.3.1 Symmetric Ohmic system in the scaling limit -- 21.3.2 Weak Ohmic damping and moderate-to-high temperature -- 21.3.3 The super-ohmic case -- 21.4 Weak-coupling theory beyond the NIBA for a biased system -- 21.4.1 The one-boson self-energy .

21.4.2 Populations and coherences (super-ohmic and Ohmic).