Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

Abstract

We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined.

arXiv comment17 pages, to appear in JPSJ

References in corpus (8)

• Coherent control of macroscopic quantum states in a single-Cooper-pair box
• Butterfly hysteresis loop and dissipative spin reversal in the S=1/2, V15 molecular complex
• Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators
• Hysteresis loops and adiabatic Landau-Zener-Stückelberg transitions in the magnetic molecule V${}_6$
• Magnetic Foehn Effect in Nonadiabatic Transition
• On the Assumption of Initial Factorization in the Master Equation for Weakly Coupled Systems I: General Framework
• On the Assumption of Initial Factorization in the Master Equation for Weakly Coupled Systems II: Solvable Models
• Synchronized pulse control of decoherence

Cited by in corpus (45)

• Nonequilibrium Green's function method for quantum thermal transport
• Open quantum system dynamics and the mean force Gibbs state
• Steady-state coherences by composite system-bath interactions
• The equilibrium states of open quantum systems in the strong coupling regime
• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
• The Accuracy of Perturbative Master Equations
• Effective Floquet-Gibbs states for dissipative quantum systems
• Charging assisted by thermalization
• Reduced density matrix for nonequilibrium steady states: A modified Redfield solution approach
• Lindbladian approximation beyond ultra-weak coupling
• Canonically consistent quantum master equation
• Master equation approach to line shape in dissipative systems
• Canonical versus noncanonical equilibration dynamics of open quantum systems
• Roadmap on Quantum Thermodynamics
• Approach to equilbrium in nano-scale systems at finite temperatur
• Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations
• Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
• Relaxation, thermalization and Markovian dynamics of two spins coupled to a spin bath
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir
• Exactness of the mean-field dynamics in optical cavity systems
• Steady state thermodynamics of two qubits strongly coupled to bosonic environments
• Quantum Control in Open and Periodically Driven Systems
• Perturbative Steady States of Completely Positive Quantum Master Equations
• Dynamics of open quantum spin systems: An assessment of the quantum master equation approach
• Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate
• Spin rectification in thermally driven XXZ spin chain via the spin-Seebeck effect
• Floquet-Gibbs state in open quantum systems
• Corrections to the Hamiltonian induced by finite-strength coupling to the environment
• Strong Coupling and non-Markovian Effects in the Statistical Notion of Temperature
• Enhanced entanglement in multi-bath spin-boson models
• Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
• Anisotropic signatures in the spin-boson model
• Master equation based steady-state cluster perturbation theory
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Natural correlation between a system and a thermal reservoir
• Global becomes local: Efficient many-body dynamics for global master equations
• Strong Markov dissipation in driven-dissipative quantum systems
• The Rigorous Stochastic Matrix Multiplication Scheme for the Calculations of Reduced Equilibrium Density Matrices of Open Multilevel Quantum Systems
• Distribution of eigenstate populations and dissipative beating dynamics in uniaxial single-spin magnets
• On the difference between thermalization in open and isolated quantum systems: a case study
• Decoherence of Majorana zero modes mediated by gapless fermions