Fernengel, Bernd ; Drossel, Barbara (2021)
Bifurcations and chaos in nonlinear Lindblad equations.
In: Journal of Physics A: Mathematical and Theoretical, 2020, 53 (38)
doi: 10.26083/tuprints-00019336
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the dynamics of the density matrix is of a quantum system results not only from the interaction with an external environment, but also with other quantum systems of the same type, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. As specific examples that display the various types of dynamical behavior, we suggest explicit models based on systems of interacting spins at finite temperature and exposed to amagnetic field that can change in dependence of the magnetization. Due to the interaction between spins, which is treated at mean-field level, the Hamiltonian as well as the transition rates of the Lindblad equation become dependent on the density matrix.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Fernengel, Bernd ; Drossel, Barbara |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Bifurcations and chaos in nonlinear Lindblad equations |
| Sprache: | Englisch |
| Publikationsjahr: | 2021 |
| Publikationsdatum der Erstveröffentlichung: | 2020 |
| Verlag: | IOP Publishing |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Physics A: Mathematical and Theoretical |
| Jahrgang/Volume einer Zeitschrift: | 53 |
| (Heft-)Nummer: | 38 |
| Kollation: | 20 Seiten |
| DOI: | 10.26083/tuprints-00019336 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/19336 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung aus gefördertem Golden Open Access |
| Kurzbeschreibung (Abstract): | The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the dynamics of the density matrix is of a quantum system results not only from the interaction with an external environment, but also with other quantum systems of the same type, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. As specific examples that display the various types of dynamical behavior, we suggest explicit models based on systems of interacting spins at finite temperature and exposed to amagnetic field that can change in dependence of the magnetization. Due to the interaction between spins, which is treated at mean-field level, the Hamiltonian as well as the transition rates of the Lindblad equation become dependent on the density matrix. |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-193362 |
| Zusätzliche Informationen: | Keywords: Lindblad equation, quantum dynamics, nonlinear dynamics, bifurcations |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Physik Kondensierter Materie (IPKM) |
| Hinterlegungsdatum: | 23 Aug 2021 12:17 |
| Letzte Änderung: | 01 Sep 2021 10:42 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Bifurcations and chaos in nonlinear Lindblad equations. (deposited 23 Aug 2021 12:17) [Gegenwärtig angezeigt]
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