Spectral and steady-state properties of fermionic random quadratic Liouvillians

Costa, João (author), Ribeiro, Pedro (author), De Luca, Andrea (author), Prosen, Tomaž (author), Sá, Lucas (author)

We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by $M$ random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, $m=M/(2N_F)$, we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for $m=1/2$ and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below $m=1/2$, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.

• Language: English
• Keywords: statistical mechanics, dissipative systems, ergidicity, open quantum systems
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication version: Version of Record
• Publication date: 09.10.2023
• Year: 2023
• Number of pages: 41 str.
• Numbering: Vol. 15, iss. 4, art. no. 145
• PID: 20.500.12556/RUL-155485
• UDC: 536.93
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.15.4.145
• COBISS.SI-ID: 191408131
• Publication date in RUL: 04.04.2024

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: statistična mehanika, disipativni sistemi, ergodičnost, odprti kvantni sistemi

Projects

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

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0402-2019
• Name: Matematična fizika