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Quantum Dissipative Systems.

By: Series: Series in Modern Condensed Matter Physics SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2008Copyright date: ©2008Edition: 3rd edDescription: 1 online resource (527 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9789812791795
Subject(s): Genre/Form: Additional physical formats: Print version:: Quantum Dissipative SystemsDDC classification:
  • 530.12
LOC classification:
  • QC174.12.W45 2008
Online resources:
Contents:
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.
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.
Summary: Key Features:Contains changes, extensions, and additions from the second edition to better meet the requests of both newcomers to the field and advanced readersFocuses on nonequilibrium quantum transport in quantum impurity systems from the viewpoint of dissipative quantum mechanicsPresents a broad perspective to open up this rapidly developing field to interested researchers normally working in different fields.
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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.

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.

Key Features:Contains changes, extensions, and additions from the second edition to better meet the requests of both newcomers to the field and advanced readersFocuses on nonequilibrium quantum transport in quantum impurity systems from the viewpoint of dissipative quantum mechanicsPresents a broad perspective to open up this rapidly developing field to interested researchers normally working in different fields.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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