Dynamics of Open Quantum Systems II, Markovian Approximation

• URL: http://arxiv.org/abs/2105.00023v2
• Date: Wed, 29 Dec 2021 16:37:45 GMT
• Title: Dynamics of Open Quantum Systems II, Markovian Approximation
• Authors: Marco Merkli
• Abstract summary: We show that for fixed, small values of the coupling constant $lambda$, the true reduced dynamics of the system is approximated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is $O(lambda|1/4)$ for all times.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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