Time Dependent Markovian Quantum Master Equation

TL;DR

This paper develops a non-adiabatic Markovian quantum master equation (NAME) for driven systems coupled to thermal baths, extending validity beyond adiabatic limits and revealing effects on coherence and thermalization.

Contribution

The paper introduces the Non-Adiabatic Master Equation (NAME), a new derivation that accounts for non-adiabatic driving in quantum systems, improving upon previous adiabatic models.

Findings

NAME predicts coherence emergence due to dissipation.

Non-adiabatic driving suppresses thermalization rate.

Comparison shows NAME aligns well with numerical results.

Abstract

We construct a quantum Markovian Master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the Master equation to be extended beyond the adiabatic limit. The Non-Adiabatic Master Equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic Master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the non-adiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic Master equation.