Universal signature from integrability to chaos in dissipative open quantum systems

Akemann, Gernot (author), Kieburg, Mario (author), Mielke, Adam (author), Prosen, Tomaž (author)

We study the transition between integrable and chaotic behavior in dissipative open quantum systems, exemplified by a boundary driven quantum spin chain. The repulsion between the complex eigenvalues of the corresponding Liouville operator in radial distance $s$ is used as a universal measure. The corresponding level spacing distribution is well fitted by that of a static two-dimensional Coulomb gas with harmonic potential at inverse temperature $\beta \in [0,2]$. Here, $\beta=0$ yields the two-dimensional Poisson distribution, matching the integrable limit of the system, and $\beta=2$ equals the distribution obtained from the complex Ginibre ensemble, describing the fully chaotic limit. Our findings generalize the results of Grobe, Haake, and Sommers, who derived a universal cubic level repulsion for small spacings $s$. We collect mathematical evidence for the universality of the full level spacing distribution in the fully chaotic limit at $\beta=2$. It holds for all three Ginibre ensembles of random matrices with independent real, complex, or quaternion matrix elements.

• Language: English
• Keywords: quantum mechanics, quantum chaos, open quantum systems, nonlinear dynamics, statistical physics
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2019
• Number of pages: Str. 254101-1-254101-6
• Numbering: Vol. 123, iss. 25
• PID: 20.500.12556/RUL-113303
• UDC: 530.182
• ISSN on article: 0031-9007
• DOI: 10.1103/PhysRevLett.123.254101
• COBISS.SI-ID: 3395940
• Publication date in RUL: 19.12.2019

Record is a part of a journal

• Title: Physical review letters
• Shortened title: Phys. rev. lett.
• Publisher: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, kvantni kaos, odprti kvantni sistemi, nelinearna dinamika, statistična fizika

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