Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application

Fiorelli, Eliana; Müller, Markus; Lesanovsky, Igor; Carollo, Federico

Abstract

We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ‘state-dependent’ rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-) local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.

Citation

Fiorelli, E., Müller, M., Lesanovsky, I., & Carollo, F. (2023). Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application. New Journal of Physics, 25(8), Article 083010. https://doi.org/10.1088/1367-2630/ace470

• Journal Article Type: Article
• Acceptance Date: Jul 5, 2023
• Online Publication Date: Aug 2, 2023
• Publication Date: 2023-08
• Deposit Date: Jul 16, 2023
• Publicly Available Date: Aug 2, 2023
• Journal: New Journal of Physics
• Electronic ISSN: 1367-2630
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 8
• Article Number: 083010
• DOI: https://doi.org/10.1088/1367-2630/ace470
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/22726720
• Publisher URL: https://iopscience.iop.org/article/10.1088/1367-2630/ace470
• Additional Information: This is the peer reviewed version of the following article: Fiorelli, E., Müller, M., Lesanovsky, I., & Carollo, F. (2023). Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application. New Journal of Physics, 25, Article 083010, which has been published in final form at https://doi.org/10.1088/1367-2630/ace470