Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1

Transcription

1 xi Contents Preface Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii viii ix 1 Introduction 1 I GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5 Diverse limited approaches: a brief survey 5.1 Langevin equation for a damped classical system New schemes of quantization Traditional system-plus-reservoir methods Quantum-mechanical master equations for weak coupling Lindblad theory Operator Langevin equations for weak coupling Generalized quantum Langevin equation Generalized quasiclassical Langevin equation Phenomenological methods Stochastic dynamics in Hilbert space System-plus-reservoir models Harmonic oscillator bath with linear coupling The Hamiltonian of the global system The road to generalized Langevin equations Phenomenological modeling of friction Quantum statistical properties of the stochastic force Displacement correlation function Thermal propagator and imaginary-time correlations Ohmic and frequency-dependent damping Fractional Langevin equation Rubin model Interaction of a charged particle with the radiation field

2 xii CONTENTS 3. Ergodicity The spin-boson model The model Hamiltonian Flux and charge qubits: reduction to the spin-boson model Microscopic models Acoustic polaron: one-phonon and two-phonon coupling Optical polaron Interaction with fermions (normal and superconducting) Superconducting tunnel junction Charging and environmental effects in tunnel junctions The global system for single electron tunneling Resistor, inductor, and transmission lines Charging effects in junctions Nonlinear quantum environments Imaginary-time approach and equilibrium dynamics General concepts Density matrix and reduced density matrix Imaginary-time path integral Effective action and equilibrium density matrix Open system with bilinear coupling to a harmonic reservoir State-dependent memory friction Spin-boson model Acoustic polaron and defect tunneling: one-phonon coupling Acoustic polaron: two-phonon coupling Tunneling between surfaces: one-phonon coupling Optical polaron Heavy particle in a metal Heavy particle in a superconductor Effective action of a junction Electromagnetic environment Partition function of the open system General path integral expression Semiclassical approximation Partition function of the damped harmonic oscillator Functional measure in Fourier space Partition function of the damped harmonic oscillator revisited Quantum statistical expectation values in phase space Generalized Weyl correspondence Generalized Wigner function and expectation values

3 CONTENTS xiii 5 Real-time path integrals and nonequilibrium dynamics Statement of the problem and general concepts Feynman-Vernon method for a product initial state Decoherence and friction General initial states and preparation function Complex-time path integral for the propagating function Real-time path integral for the propagating function Closed time contour representation Complex-time path Real-time path Semiclassical regime Extremal paths Quasiclassical Langevin equation Stochastic unraveling of influence functionals Non-Markovian dissipative dynamics in the semiclassical limit Van Vleck and Herman-Kluk propagator Semiclassical dissipative dynamics Brief summary and outlook II MISCELLANEOUS APPLICATIONS Damped linear quantum mechanical oscillator Fluctuation-dissipation theorem Stochastic modeling Susceptibility Ohmic friction Ohmic friction with Drude cutoff Radiation damping The position autocorrelation function Ohmic friction Non-Ohmic spectral density Shiba relation Partition function and implications Partition function Internal energy, free energy, and entropy Specific heat and Wilson ratio Spectral density of states Mean square of position and momentum General expressions for colored noise Ohmic friction Ohmic friction with Drude cutoff Equilibrium density matrix

4 xiv CONTENTS Derivation of the action Purity Quantum master equations for the reduced density matrix Thermal initial condition Product initial state Approximate time-independent Liouville operators Connection with Lindblad theory Quantum Brownian free motion Spectral density, damping function and mass renormalization Displacement correlation and response function Ohmic friction Response function Mean square displacement Momentum spread Frequency-dependent friction Response function and mobility Mean square displacement Partition function and thermodynamic properties Partition function Internal and free energy Specific heat Spectral density of states The thermodynamic variational approach Centroid and the effective classical potential Centroid The effective classical potential Variational method Variational method for the free energy Variational method for the effective classical potential Variational perturbation theory Expectation values in coordinate and phase space Suppression of quantum coherence Nondynamical versus dynamical environment Suppression of transversal and longitudinal interferences Decoherence in the semiclassical picture A model with localized bath modes Dephasing rate formula Statistical average of paths Ballistic motion Diffusive motion

5 CONTENTS xv 9.4 Decoherence of electrons III QUANTUM STATISTICAL DECAY 1 10 Introduction 1 11 Classical rate theory: a brief overview Classical transition state theory Moderate-to-strong-damping regime Strong damping regime Weak-damping regime Quantum rate theory: basic methods Formal rate expressions in terms of flux operators Quantum transition state theory Semiclassical limit Quantum tunneling regime Free energy method Centroid method Multidimensional quantum rate theory The global metastable potential Periodic orbit and bounce Crossover from thermal to quantum decay Normal mode analysis at the barrier top Turnover theory for activated rate processes The crossover temperature Thermally activated decay Rate formula above the crossover regime Quantum corrections in the pre-exponential factor The quantum Smoluchowski equation approach Multidimensional quantum transition state theory The crossover region Beyond steepest descent above T Beyond steepest descent below T The scaling region

6 xvi CONTENTS 17 Dissipative quantum tunneling The quantum rate formula Thermal enhancement of macroscopic quantum tunneling Quantum decay in a cubic potential for Ohmic friction Bounce action and quantum mechanical prefactor Analytic results for strong Ohmic dissipation Quantum decay in a tilted cosine potential The case of weak bias Concluding remarks IV THE DISSIPATIVE TWO-STATE SYSTEM Introduction Truncation of the double-well to the two-state system Shifted oscillators and orthogonality catastrophe Adiabatic renormalization Instanton in a double parabolic well Renormalized tunneling matrix element Polaron transformation Pair interaction in the charge picture Analytic expression for spectral density with any power s Ohmic dissipation and universality limit Thermodynamics Partition function and specific heat Exact formal expression for the partition function Static susceptibility and specific heat The self-energy method The limit of high temperatures Noninteracting kink-pair approximation Weak-damping limit The self-energy method revisited: partial resummation Ohmic dissipation Specific heat and Wilson ratio The special case K = Non-Ohmic spectral densities The sub-ohmic case The super-ohmic case Relation between the Ohmic TSS and the Kondo model Anisotropic Kondo model Resonance level model Equivalence of the Ohmic TSS with the 1/r Ising model

7 CONTENTS xvii 0 Electron transfer and incoherent tunneling Electron transfer Adiabatic bath Marcus theory for electron transfer Incoherent tunneling in the nonadiabatic regime General expressions for the nonadiabatic rate Probability for energy exchange: general results The spectral probability density for absorption at T = Crossover from quantum-mechanical to classical behavior The Ohmic case Exact nonadiabatic rates for K = 1 and K = The sub-ohmic case (0 <s<1) The super-ohmic case (s >1) Incoherent defect tunneling in metals Single charge tunneling Weak-tunneling regime The current-voltage characteristics Weak tunneling of 1D interacting electrons Tunneling of Cooper pairs Tunneling of quasiparticles Two-state dynamics: basics and methods Initial preparation, expectation values, and correlations Product initial state Thermal initial state Exact formal expressions for the system dynamics Sojourns and blips Conditional propagating functions The expectation values σ j t (j = x, y, z) Correlation and response function of the populations Correlation and response function of the coherences Generalized exact master equation and integral relations The noninteracting-blip approximation (NIBA) Assumptions Limitations The interacting-blip chain approximation (IBCA) Two-state dynamics: sundry topics 39.1 Symmetric TSS in the NIBA Ohmic scaling limit The super-ohmic case White-noise regime Power spectrum of the stochastic force

8 xviii CONTENTS.. Symmetric Ohmic TSS at moderate-to-high temperature Biased Ohmic TSS at moderate-to-high temperature Weak quantum noise in the biased TSS The one-boson self-energy Populations and coherences (super-ohmic and Ohmic) Pure dephasing /f noise and decoherence /f noise from fluctuating background charges /f noise from coherent two-level systems Decoherence from 1/f noise The Ohmic TSS at and close to the Toulouse point Grand-canonical sums of collapsed blips and sojourns The expectation value σ z t for K = The case K = 1 κ; coherent-incoherent crossover Equilibrium σ z autocorrelation function Equilibrium σ x autocorrelation function Correlation functions in the Toulouse model Long-time behavior at T = 0forK < 1: general discussion The populations The population correlations and Shiba relation The coherence correlation function From weak to strong tunneling: relaxation and decoherence Incoherent tunneling beyond the nonadiabatic limit Decoherence at zero temperature: analytic results Thermodynamics from dynamics The driven two-state system Time-dependent external fields Diagonal and off-diagonal driving Exact formal solution Linear response The Ohmic case with Kondo parameter K = Markovian regime High-frequency regime Quantum stochastic resonance Driving-induced symmetry breaking V THE DISSIPATIVE MULTI-STATE SYSTEM Quantum Brownian particle in a washboard potential Introduction Weak- and tight-binding representation

9 CONTENTS xix 5 Multi-state dynamics Quantum transport and quantum-statistical fluctuations Product initial state Characteristic functions of moments and cumulants Thermal initial state and correlation functions Poissonian quantum transport Incoherent nearest-neighbor transitions (weak tunneling) The general case (strong tunneling) Exact formal expressions for the system dynamics Product initial state Thermal initial state Mobility and Diffusion Exact formal series expressions for transport coefficients Einstein relation The Ohmic case Weak-tunneling regime Weak-damping limit Exact solution in the Ohmic scaling limit at K = Current and mobility Diffusion and skewness The effects of a thermal initial state Mean position and variance Linear response The exactly solvable case K = Duality symmetry Duality for general spectral density The map between the TB and WB Hamiltonian Frequency-dependent linear mobility Nonlinear static mobility Self-duality in the exactly solvable cases K = 1 and K = Full counting statistics at K = Full counting statistics at K = Duality and supercurrent in Josephson junctions Charge-phase duality Supercurrent-voltage characteristics for ρ Supercurrent-voltage characteristics at ρ = Supercurrent-voltage characteristics at ρ = Self-duality in the Ohmic scaling limit Linear mobility at finite T Nonlinear mobility at T = Exact scaling function at T = 0 for arbitrary K

10 xx CONTENTS Construction of the self-dual scaling solution Supercurrent-voltage characteristics at T = 0 for arbitrary ρ Connection with Seiberg-Witten theory Special limits Full counting statistics at zero temperature Low temperature behavior of the characteristic function Twisted partition function and nonlinear mobility Solving the imaginary-time Coulomb gas with Jack polynomials Nonlinear mobility Strong barrier limit The case K The limit T Charge transport in quantum impurity systems Generic models for transmission of charge through barriers The Tomonaga-Luttinger liquid Charge transport through a single weak barrier Charge transport through a single strong barrier Coherent conductor in an Ohmic environment Equivalence with quantum transport in a washboard potential Self-duality between weak and strong tunneling Full counting statistics of charge transfer Charge transport at low temperature for arbitrary g Full counting statistics at g = 1 and general temperature Quantum transport for sub- and super-ohmic friction Tight-binding representation Sub-Ohmic friction Super-Ohmic friction Weak-binding representation Super-Ohmic friction Sub-Ohmic friction Bibliography 539 Index 561