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Time Dependent Markovian Quantum Master Equation

Roie Dann, Amikam Levy, Ronnie Kosloff

We construct a quantum Markovian Master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the driven system propagator, extending the validity beyond the adiabatic limit. The Non Adiabatic Master Equation (NAME) is derived employing the weak system-bath coupling limit. In addition, the NAME is valid when a separation of time-scale exists between the bath dynamics and the external driving. In contrast to the adiabatic Master equation, the NAME couples population and coherence. We employ the NAME to solve the thematic example of an open driven time-dependent harmonic oscillator. Unlike the standard Master equation, for the harmonic oscillator the NAME predicts emergence of coherence associated with both the dissipative and unitary terms. In addition, the thermalization rate is slowed down as a result of the driving. The solution is checked by comparing to both numerical calculations and to the adiabatic Master equation.

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ArXiv number: 1805.10689