Spectral and steady-state properties of random Liouvillians

Sá, Lucas (author), Ribeiro, Pedro (author), Prosen, Tomaž (author)

We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular quantity. Within each regime, we determine the scaling exponents with the dissipation strength and system size. We find that, for two or more dissipation channels, the spectral gap increases with the system size. The spectral distribution of the steady state is Poissonian at low dissipation strength and conforms to that of a random matrix once the dissipation is sufficiently strong. Our results can help to understand the long-time dynamics and steady-state properties of generic dissipative systems.

• Language: English
• Keywords: open quantum systems, quantum chaos
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: 20 str.
• Numbering: Vol. 53, art. no. 305303
• PID: 20.500.12556/RUL-117819
• UDC: 530.145
• ISSN on article: 1751-8113
• DOI: 10.1088/1751-8121/ab9337
• COBISS.SI-ID: 23780099
• Publication date in RUL: 28.07.2020

SÁ, Lucas, RIBEIRO, Pedro and PROSEN, Tomaž, 2020, Spectral and steady-state properties of random Liouvillians. Journal of physics : Mathematical and theoretical [online]. 2020. Vol. 53, no. 305303. [Accessed 19 April 2025]. DOI 10.1088/1751-8121/ab9337. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=117819

Record is a part of a journal

• Title: Journal of physics : Mathematical and theoretical
• Shortened title: J. phys., A, Math. theor.
• Publisher: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

Secondary language

• Language: Slovenian
• Keywords: odprti kvantni sistemi, kvantni kaos

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika