Bath induced coherence and the secular approximation
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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 inter-system 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 to different Markovian master equations, we find that a smooth crossover of the equations-of-motion between dominant inter-system and system-bath coupling exists - but requires a non-secular master equation. We predict a singular behaviour of the dynamics, and show that the ultimate failure of non-secular equations of motion is essentially a failure of the Markov approximation. Our findings justify the use of time-local theories throughout the crossover between system-bath dominated and inter-system-coupling dominated dynamics.
Eastham , P R , Kirton , P , Cammack , H M , Lovett , B W & Keeling , J 2016 , ' Bath induced coherence and the secular approximation ' , Physical Review. A, Atomic, molecular, and optical physics , vol. 94 , no. 1 , 012110 . https://doi.org/10.1103/PhysRevA.94.012110
Physical Review. A, Atomic, molecular, and optical physics
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