Nonlinear extension of the quantum dynamical semigroup

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 quasilinear 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.

Automated summary

This paper discusses deterministic nonlinear time evolutions satisfying convex quasi-linearity condition, proving that a family of linear non-trace-preserving maps satisfying the semigroup property will generate a family of convex quasilinear operations with the same property. The Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution is generalized, with examples including general qubit evolution and extension of the Jaynes-Cummings model. The formalism is applied to spin density matrix of a charged particle in an electromagnetic field and flavor evolution of solar neutrinos.