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Emergence of jumps in quantum trajectories via homogeneization

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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https://hal.archives-ouvertes.fr/hal-03157272
Contributor : Tristan Benoist Connect in order to contact the contributor
Submitted on : Wednesday, March 3, 2021 - 9:09:58 AM
Last modification on : Tuesday, October 19, 2021 - 11:17:07 PM

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Tristan Benoist, Cedric Bernardin, Raphaël Chétrite, Reda Chhaibi, Joseph Najnudel, et al.. Emergence of jumps in quantum trajectories via homogeneization. Communications in Mathematical Physics, Springer Verlag, In press, ⟨10.1007/s00220-021-04179-8⟩. ⟨hal-03157272⟩

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