Emergence of jumps in quantum trajectories via homogeneization
arXiv:2103.01916 · doi:10.1007/s00220-021-04179-8
Abstract
In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct time scales, we start by describing a homogenized limiting semi-group. This result is of independent interest and is formulated outside of the scope of quantum trajectories. Going back to the quantum context, we show that, in the Meyer-Zheng topology, the time-continuous quantum trajectories converge weakly to the discontinuous trajectories of a pure jump Markov process. Notably, this convergence cannot hold in the usual Skorokhod topology.
arXiv comment48 pages, no figures. v1: Preliminary version. v2: Minor changes in presentation, submitted version
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