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.

17 pages, to appear in JPSJ

References in corpus (2)

• 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

Cited by in corpus (24)

• Open quantum system dynamics and the mean force Gibbs state
• 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
• Canonically consistent quantum master equation
• Roadmap on Quantum Thermodynamics
• Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations
• Relaxation, thermalization and Markovian dynamics of two spins coupled to a spin bath
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• Quantum Control in Open and Periodically Driven Systems
• Perturbative Steady States of Completely Positive Quantum Master Equations
• Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate
• Corrections to the Hamiltonian induced by finite-strength coupling to the environment
• Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
• Enhanced entanglement in multi-bath spin-boson models
• Anisotropic signatures in the spin-boson model
• 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
• Global becomes local: Efficient many-body dynamics for global master equations
• Strong Markov dissipation in driven-dissipative quantum systems
• On the difference between thermalization in open and isolated quantum systems: a case study
• Decoherence of Majorana zero modes mediated by gapless fermions