Quantum dissipative systems
Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool...
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| Format | eBook Book |
| Language | English |
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Singapore
World Scientific Publishing Co. Pte. Ltd
2008
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC WSPC World Scientific Publishing |
| Edition | 3rd ed. |
| Series | Series in modern condensed matter physics |
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| Abstract | Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book — originally published in 1990 and republished in 1999 as an enlarged second edition — delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. |
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| AbstractList | Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions - delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems.This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.Sample Chapter(s)Chapter 1: Introduction (85 KB)Chapter 2: Diverse Limited Approaches: A Brief Survey (235 KB)Contents: IntroductionGeneral Theory of Open Quantum Systems:Diverse Limited Approaches: A Brief SurveySystem-Plus-Reservoir ModelsImaginary-Time Approach and Equilibrium DynamicsReal-Time Path Integrals and Nonequilibrium DynamicsMiscellaneous Applications:Damped Linear Quantum Mechanical OscillatorQuantum Brownian Free MotionThe Thermodynamic Variational ApproachSuppression of Quantum CoherenceQuantum Statistical Decay:IntroductionClassical Rate Theory: A Brief OverviewQuantum Rate Theory: Basic Methods Multidimensional Quantum Rate TheoryCrossover From Thermal to Quantum DecayThermally Activated DecayThe Crossover RegionDissipative Quantum TunnelingThe Dissipative Two-State System:IntroductionThermodynamicsElectron Transfer and Incoherent TunnelingTwo-State Dynamics: Basics and MethodsTwo-State Dynamics: Sundry TopicsThe Driven Two-State SystemThe Dissipative Multi-State System:Quantum Brownian Particle in a Washboard PotentialMulti-State DynamicsDuality SymmetryTwisted Partition Function and Nonlinear MobilityCharge Transport in Quantum Impurity SystemsQuantum Transport for Sub- and Super-Ohmic FrictionReadership: Advanced undergraduate and graduate students; researchers in quantum statistical and condensed matter physics, in quantum/classical mechanics, in quantum information and quantum state engineering, in quantum optics, and in Bose-condensed systems. Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 as an enlarged second edition - delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. In this third edition, 26 chapters from the second edition contain additional material and several chapters are completely rewritten. It deals with the phenomena and theory of decoherence, relaxation, and dissipation in quantum mechanics that arise from the interaction with the environment. In so doing, a general path integral description of equilibrium thermodynamics and nonequilibrium dynamics is developed. Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book - originally published in 1990 and republished in 1999 as an enlarged second edition - delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments.In this third edition, 26 chapters from the second edition contain additional material and several chapters are completely rewritten. It deals with the phenomena and theory of decoherence, relaxation, and dissipation in quantum mechanics that arise from the interaction with the environment. In so doing, a general path integral description of equilibrium thermodynamics and nonequilibrium dynamics is developed.Sample Chapter(s)Introduction (262 KB)Contents: General Theory of Open Quantum SystemsFew Sample ApplicationsQuantum Statistical DecayThe Dissipative Two-State SystemThe Dissipative Multi-State SystemReadership: Advanced undergraduate and graduate students as well as researchers in quantum-statistical and condensed matter physics, quantum/classical mechanics, quantum information and computation, and quantum optics. Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. Today, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book — originally published in 1990 and republished in 1999 as an enlarged second edition — delves much deeper than ever before into the fundamental concepts, methods, and applications of quantum dissipative systems, including the most recent developments. |
| Author | Weiss, Ulrich |
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| Keywords | Thermodynamics Quantum Mechanics Quantum Tunneling Quantum System |
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| Notes | Includes bibliographical references (p. 539-560) and index |
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| Snippet | Major advances in the quantum theory of macroscopic systems, in combination with stunning experimental achievements, have brightened the field and brought it... Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in... |
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| SubjectTerms | Mathematical physics Path integrals Quantum statistics Quantum theory Thermodynamics |
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| TableOfContents | Quantum dissipative systems -- Preface -- Preface to the Second Edition -- Acknowledgements -- Preface to the First Edition -- Contents -- 1. Introduction -- Part I: General Theory of Open Quantum Systems; 2. Diverse limited approaches: a brief survey -- 3. System-plus-reservoir models -- 4. Imaginary-time path integrals and statistical mechanics -- 5. Real-time path integrals and dynamics -- Part II: FEW Simple Applications; 6. Damped harmonic oscillator -- 7. Quantum Brownian free motion -- 8. The thermodynamic variational approach -- 9. Suppression of quantum coherence -- Part III: Quantum Statistical Decay; 10. Introduction -- 11. Classical rate theory: a brief overview -- 12. Quantum rate theory: basic methods -- 13. Multidimensional quantum rate theory -- 14. Crossover from thermal to quantum decay -- 15. Thermally activated decay -- 16. The crossover region -- 17. Dissipative quantum tunneling -- Part IV: The Dissipative Two-State System; 18. Introduction -- 19. Thermodynamics -- 20. Electron transfer and incoherent tunneling -- 21. Two-state dynamics -- 22. The driven two-state system -- Part V: The Dissipative Multi-State System; 23. Quantum Brownian particle in a washboard potential -- 24. Multi-state dynamics -- 25. Duality symmetry -- 26. Charge transport in quantum impurity systems -- Bibliography -- Index. Intro -- 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 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 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 < -- s < -- 1) -- 20.2.8 The super-ohmic case ( s > -- 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 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 21.4 Weak-coupling theory beyond the NIBA for a biased system 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 20.1.2 Marcus theory for electron transfer 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 Intro -- 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 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 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 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 |
| Title | Quantum dissipative systems |
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