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Journal of Statistical Physics

Interacting Quantum and Classical Continuous Systems I. The Piecewise Deterministic Dynamics

Ph. Blanchard, Robert Olkiewicz

Published Mar 1, 1999• 13 citations
Publisher
DOI
10.1023/a:1004587117602

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Abstract From the perspective of Markovian piecewise deterministic processes (PDPs), we investigate the derivation of a kinetic uncertainty relation (KUR), which was originally proposed in Markovian open quantum systems. First, stationary distributions of classical PDPs are explicitly constructed. Then, a tilting method is used to derive a rate functional of large deviations. Finally, based on an improved approximation scheme, we recover the KUR. These classical results are directly extended to the open quantum systems. We use a driven two-level quantum system to exemplify the quantum results.