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...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-03-23-420/pdf/ |
| _version_ | 1818414918464962560 |
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| author | Jakub Rembieliński Paweł Caban |
| author_facet | Jakub Rembieliński Paweł Caban |
| author_sort | Jakub Rembieliński |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T11:26:44Z |
| format | Article |
| id | doaj.art-6e5788c2d12b42519579ea693c3203f7 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-14T11:26:44Z |
| publishDate | 2021-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-6e5788c2d12b42519579ea693c3203f72022-12-21T23:03:31ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-03-01542010.22331/q-2021-03-23-42010.22331/q-2021-03-23-420Nonlinear extension of the quantum dynamical semigroupJakub RembielińskiPaweł CabanIn 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.https://quantum-journal.org/papers/q-2021-03-23-420/pdf/ |
| spellingShingle | Jakub Rembieliński Paweł Caban Nonlinear extension of the quantum dynamical semigroup Quantum |
| title | Nonlinear extension of the quantum dynamical semigroup |
| title_full | Nonlinear extension of the quantum dynamical semigroup |
| title_fullStr | Nonlinear extension of the quantum dynamical semigroup |
| title_full_unstemmed | Nonlinear extension of the quantum dynamical semigroup |
| title_short | Nonlinear extension of the quantum dynamical semigroup |
| title_sort | nonlinear extension of the quantum dynamical semigroup |
| url | https://quantum-journal.org/papers/q-2021-03-23-420/pdf/ |
| work_keys_str_mv | AT jakubrembielinski nonlinearextensionofthequantumdynamicalsemigroup AT pawełcaban nonlinearextensionofthequantumdynamicalsemigroup |