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arXiv quant-ph/05050172005-05quant-ph

The Inner Limit of Quantum Brownian Evolution and its Relevance to Positivity

Allan Tameshtit

备注：: 11 pages v2: a generalization is provided in the form of an exact expression for the reduced density operator. In addition, the definitions of the operators M and N were changed to ensure that they yield the unit operator (instead of minus the unit operator) at t=0. Equations depending on M and N were also correspondingly changed. These changes do not affect any of the main conclusions relating to positivity

英文摘要：

The conventional quantum Brownian propagator, which describes the evolution of a system of interest bilinearly coupled to and initially uncorrelated with a reservoir, does not preserve positivity of density operators, prompting workers to modify the propagator by the ad hoc addition of time-independent terms to the corresponding generator. We show that no such terms need be added to the generator to preserve positivity provided one accounts for the rapid entanglement of the system of interest and the reservoir on a time scale too short for the conventional propagator to be valid.

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