Nonlinear extension of the quantum dynamical semigroup

• URL: http://arxiv.org/abs/2003.09170v3
• Date: Thu, 18 Mar 2021 21:57:14 GMT
• Title: Nonlinear extension of the quantum dynamical semigroup
• Authors: Jakub Rembieli\'nski and Pawe{\l} Caban
• Abstract summary: We consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.

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