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Bifurcations and chaos in nonlinear Lindblad equations

Fernengel, Bernd ; Drossel, Barbara (2021):
Bifurcations and chaos in nonlinear Lindblad equations. (Publisher's Version)
In: Journal of Physics A: Mathematical and Theoretical, 53 (38), IOP Publishing, ISSN 0022-3689, e-ISSN 1751-8113,
DOI: 10.26083/tuprints-00019336,
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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Status: Publisher's Version
Title: Bifurcations and chaos in nonlinear Lindblad equations
Language: English
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.

Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Journal volume: 53
Number: 38
Publisher: IOP Publishing
Collation: 20 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute for Condensed Matter Physics
Date Deposited: 23 Aug 2021 12:17
Last Modified: 23 Aug 2021 13:52
DOI: 10.26083/tuprints-00019336
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-193362
Additional Information:

Keywords: Lindblad equation, quantum dynamics, nonlinear dynamics, bifurcations

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19336
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