Universal signature from integrability to chaos in dissipative open quantum systems
ID Akemann, Gernot (Author), ID Kieburg, Mario (Author), ID Mielke, Adam (Author), ID Prosen, Tomaž (Author)

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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.

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
Number of pages:Str. 254101-1-254101-6
Numbering:Vol. 123, iss. 25
PID:20.500.12556/RUL-113303 This link opens in a new window
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.123.254101 This link opens in a new window
COBISS.SI-ID:3395940 This link opens in a new window
Publication date in RUL:19.12.2019
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Record is a part of a journal

Title:Physical review letters
Shortened title:Phys. rev. lett.
Publisher:American Physical Society
COBISS.SI-ID:1282575 This link opens in a new window

Secondary language

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


Funder:EC - European Commission
Funding programme:H2020
Project number:694544
Name:Open many-body non-equilibrium systems

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

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