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arXiv · 0812.1507

Systematic Perturbation Theory for Dynamical Coarse-Graining

Gernot Schaller·Philipp Zedler·Tobias Brandes
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Abstract

We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical coarse-graining unconditionally preserves positivity of the density matrix -- even for bath density matrices that are not in equilibrium and also for time-dependent system Hamiltonians. By construction, the approach correctly captures the short-time dynamics, i.e., it is suitable to analyze non-Markovian effects. We compare the dynamics with the exact solution for highly non-Markovian systems and find a remarkable quality of the coarse-graining approach. The extension to higher orders is straightforward but rather tedious. The approach is especially useful for bath correlation functions of simple structure and for small system dimensions.

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Gernot Schaller, Philipp Zedler, Tobias Brandes. 2009-02-20. Systematic Perturbation Theory for Dynamical Coarse-Graining. https://doi.org/10.1103/physreva.79.032110

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