Related papers: Emergence of jumps in quantum trajectories via homogeneization

Emergence of jumps in quantum trajectories via homogeneization

URL: http://arxiv.org/abs/2103.01916v3
Date: Mon, 25 Oct 2021 07:40:03 GMT
Title: Emergence of jumps in quantum trajectories via homogeneization
Authors: Tristan Benoist, C\'edric Bernardin, Rapha\"el Chetrite, Reda Chhaibi, Joseph Najnudel, Cl\'ement Pellegrini
Abstract summary: We study the homogeneization of quantum trajectories appearing in the context of quantum measurement. 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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