We examine the properties of open quantum systems with respect to their time evolution in different regimes, Markovian and non-Markovian. We analyze their behaviour with respect to their coherent or decoherent time evolution by means of different models and try to gain some insight into the possible correlations between Markovianity and coherence.

arXiv:1503.08920Mar 31, 20154 citations

SpringerBriefs in physics

Time Evolution in Open Quantum Systems

́Angel Rivas, Susana F. Huelga

Published Sep 29, 2011• 4 citations

Publisher

DOI: 10.1007/978-3-642-23354-8_3

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For a periodically driven open quantum system, the Floquet theorem states that the time evolution operator

Λ(t,0)

of the system can be factorized as

Λ(t,0)=\mathcal{D}(t)e^{\mathcal{L}_{eff}t}

with micro-motion operator

\mathcal{D}(t)

possessing the same period as the external driving, and time-independent operator

\mathcal{L}_{eff}

. In this work, we extend this theorem to open systems that follow a modulated periodic evolution, in which the fast part is periodic while the slow part breaks the periodicity. We derive a factorization for the time evolution operator that separates the long time dynamics and the micro-motion for the open quantum system. High-frequency expansions for the effective evolution operator control the long time dynamics, and the micro-motion operator is also given and discussed. It may find applications in quantum engineering with open systems following modulated periodic evolution.