Quantum Stochastic Processes: A Case Study

Details Quantum Stochastic Processes: A Case Study Quantum Stochastic Processes: A Case Study

2011-01-18

arxiv.org/abs/1101.3472v1

J. Stat. Mech (2001) P04016

Physics

Mathematical Physics

35 pages, 1 figures

Scientific paper

We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the process allows us to specify and to construct the dilation of the quantum dynamical maps, including conditional quantum expectations. The quantum phase space Brownian motion possesses many properties similar to that of the classical Brownian motion, notably its increments are independent and identically distributed. Possible applications to dissipative phenomena in the quantum Hall effect are suggested.

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