Bath-induced coherence and the secular approximation

Eastham, P. R. and Kirton, P. and Cammack, H. M. and Lovett, B. W. and Keeling, J. (2016) Bath-induced coherence and the secular approximation. Physical Review A, 94 (1). 012110. ISSN 2469-9926 (

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Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: Does system-bath or intersystem coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution against different Markovian master equations, we find that a smooth crossover of the equations of motion between dominant intersystem and system-bath coupling exists - but it requires a nonsecular master equation. We predict singular behavior of the dynamics and show that the ultimate failure of nonsecular equations of motion is essentially a failure of the Markov approximation. Our findings support the use of time-local theories throughout the crossover between system-bath-dominated and intersystem-coupling-dominated dynamics.