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Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Univ Melbourne, Sch Math & Stat, 813 Swanston St, Melbourne, Vic 3010, Australia..
Bielefeld Univ, Fac Phys, Postfach 100131, D-33501 Bielefeld, Germany..
Univ Ljubljana, Fac Math & Phys, Phys Dept, Ljubljana 1000, Slovenia..
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 123, no 25, article id 254101Article in journal (Refereed) Published
Abstract [en]

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 Lionville 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 is an element of [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 quatemion matrix elements.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC , 2019. Vol. 123, no 25, article id 254101
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-266516DOI: 10.1103/PhysRevLett.123.254101ISI: 000503245200009PubMedID: 31922808Scopus ID: 2-s2.0-85077274428OAI: oai:DiVA.org:kth-266516DiVA, id: diva2:1391723
Note

QC 20200205

Available from: 2020-02-05 Created: 2020-02-05 Last updated: 2020-02-05Bibliographically approved

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