Nonlinear extension of the quantum dynamical semigroup

Jakub Rembieliński; Paweł Caban

doi:10.22331/q-2021-03-23-420

Nonlinear extension of the quantum dynamical semigroup

Jakub Rembieliński and Paweł Caban

Department of Theoretical Physics, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236 Łódź, Poland

Published:	2021-03-23, volume 5, page 420
Eprint:	arXiv:2003.09170v3
Doi:	https://doi.org/10.22331/q-2021-03-23-420
Citation:	Quantum 5, 420 (2021).

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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.

Featured image: Evolution of a relativistic qubit in the electromagnetic field

► BibTeX data

@article{Rembielinski2021nonlinearextension,
  doi = {10.22331/q-2021-03-23-420},
  url = {https://doi.org/10.22331/q-2021-03-23-420},
  title = {Nonlinear extension of the quantum dynamical semigroup},
  author = {Rembieli{\'{n}}ski, Jakub and Caban, Pawe{\l{}}},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {420},
  month = mar,
  year = {2021}
}

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