Nonlinear extension of the quantum dynamical semigroup

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.

15 pages, 11 figures, extended version accepted in Quantum

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• Proposal for a Lorenz qubit
• No-Signaling in Steepest Entropy Ascent: A Nonlinear Non-local Non-equilibrium Quantum Dynamics of Composite Systems
• Are intrinsic decoherence models physical theories?
• Quantum implementation of non-unitary operations with biorthogonal representations
• Linear and integrable nonlinear evolution of the qutrit