Dynamics of Open Quantum Systems II, Markovian Approximation

Abstract

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is $O(|\lambda {|}^{1/4})$ for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy $O(|\lambda {|}^{1/4})$ for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as $1/t^4$ or faster, which is a significant improvement relative to the previously required exponential decay.

Comments and explanations added according to referee requests -- version as published in journal Quantum

References in corpus (7)

• Markovian Master Equations: A Critical Study
• A Brief History of the GKLS Equation
• Open quantum system dynamics and the mean force Gibbs state
• Another Return of 'Return to Equilibrium'
• Dynamics of Open Quantum Systems I, Oscillation and Decay
• Ergodicity of the Spin-Boson Model for arbitrary coupling strength
• On the hybrid Davies like generator for quantum dissipation

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• Dynamics of Open Quantum Systems I, Oscillation and Decay
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• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Equivalence between the second order steady state for the spin-Boson model and its quantum mean force Gibbs state
• Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics
• Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization
• Detecting Markovianity of Quantum Processes via Recurrent Neural Networks
• The Adiabatic Wigner-Weisskopf Model
• Quasi-classical Limit of a Spin Coupled to a Reservoir
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
• On the difference between thermalization in open and isolated quantum systems: a case study