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Chapter 7 (Quantum Dissipation)
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Contents
Contents
Index
Quantum Dissipation
Subsections
Introduction
Motivation
Origin of Dissipation, System-Bath Theories
Example
Formal Splitting
Overview
Literature
Master Equation I: Derivation
Interaction Picture
Perturbation Theory in the System-Bath Coupling
Effective Density Matrix of the System
Equation of Motion for
Assumption (factorising initial condition):
Born Approximation
Explicit Form of Master Equation
Master Equation II: the Damped Harmonic Oscillator
Introduction
Non-RWA Model
RWA-Model
Master Equation (RWA)
Thermal Bath Correlation Functions (RWA)
Rates and Energy Shift (RWA)
Final Form of Master Equation
Expectation Values (RWA Model)
Master Equation (Non-RWA Model)
Thermal Bath Correlation Function (non-RWA)
Definition
Bosonic Spectral Density
Properties of
Validity of Markov Assumption
Derivation of Master equation (non-RWA), secular approximation
`Secular approximation'
-
Representation
Master Equation IV: Phase Space Solution Methods
-representation
Revision:
-representation
Derivation of the PDE
Solution of the PDE I: zero temperature
Solution of the PDE II: finite temperature
-representation
Remarks
Correlation Functions and the Quantum Regression Theorem
Correlation Functions
The Two-Level System I
Generic Model: Two-Level System Interacting with Bosonic Modes
System
System-Bath Interaction
Bath
Further Remarks
Atom + Electrical Field
Model Atom
Dipole Approximation
Rotating Wave Approximation (RWA)
Spontaneous Emission (Atom without Driving Field)
Model for
: Two-Level System Coupled to Photon Bath in RWA
Mapping onto harmonic oscillator master equation
Expectation Values, Einstein Equations, Bloch Equations
The Quantum Jump (Quantum Trajectory) Approach
Introduction
Motivation: telegraphic fluorescence (driven spontaneous emission) of single atoms
Unravelling and Decomposition into Histories
Super-Operators
Decomposition into Histories
`Monte Carlo' Procedure
Feynman-Vernon Influence Functional Theories
Introduction, Motivation
Single Path Integrals
Double Path Integrals
The Influence Functional
Influence Functional for Coupling to Harmonic Oscillators
Time-evolution operator
Influence Phase
Linear Response, Fluctuation-Dissipation Theorem for
Applications: Linear Coupling, Damped Harmonic Oscillator
Linear Coupling
Propagator for Damped Harmonic Oscillator
Another Look at Influence Functionals for General Baths
`Re-Exponentiation'
`Semiclassical' Limit for Damped Single Particle Motion
Expansion of the Influence Phase
Completing the Square
Wigner Distribution in `Semi-classical' Limit
Discussion
Linear Dissipation (`Ohmic Bath')
Application: Polaron-Transport
The Spin-Boson Problem
Master Equations: Some Further Remarks and Examples
Lindblad Theory
Resonance Fluorescence (Driven Dissipative Few-Level Atom)
Non-Markoffian Master Equations
Operator Langevin Equations
Tobias Brandes 2004-02-18
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Representation
-representation
-representation
: Two-Level System Coupled to Photon Bath in RWA![$ U_B[q]\equiv U_B(t)$](img11.png){kind=small}
