Systematic Perturbation Theory for Dynamical Coarse-Graining

Details Systematic Perturbation Theory for Dynamical Coarse-Graining Systematic Perturbation Theory for Dynamical Coarse-Graining

2008-12-08

arxiv.org/abs/0812.1507v2

Physical Review A 79(3), 032110, (2009)

Physics

Quantum Physics

17 pages, 5 figures, version accepted for publication in PRA

Scientific paper

10.1103/PhysRevA.79.032110

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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