Nonlinear functionals of master equation unravelings

• URL: http://arxiv.org/abs/2402.05352v1
• Date: Thu, 8 Feb 2024 02:21:23 GMT
• Title: Nonlinear functionals of master equation unravelings
• Authors: Dustin Keys, Jan Wehr
• Abstract summary: The trajectories generated by unravelings may also be treated as real -- as in the collapse models. Two types of nonlinear functionals are considered here: variance, and entropy. In the case of entropy, these corrections are shown to be negative, expressing the localization introduced by the Lindblad operators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unravelings provide a probabilistic representation of solutions of master equations and a method of computation of the density operator dynamics. The trajectories generated by unravelings may also be treated as real -- as in the stochastic collapse models. While averages of linear functionals of the unraveling trajectories can be calculated from the master equation, the situation is different for nonlinear functionals, thanks to the corrections with nonzero expected values, coming from the It\^o formula. Two types of nonlinear functionals are considered here: variance, and entropy. The corrections are calculated explicitly for two types of unravelings, based on Poisson and Wiener processes. In the case of entropy, these corrections are shown to be negative, expressing the localization introduced by the Lindblad operators.

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