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  • 1.
    Akemann, Gernot
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Kieburg, Mario
    Univ Melbourne, Sch Math & Stat, 813 Swanston St, Melbourne, Vic 3010, Australia..
    Mielke, Adam
    Bielefeld Univ, Fac Phys, Postfach 100131, D-33501 Bielefeld, Germany..
    Prosen, Tomaz
    Univ Ljubljana, Fac Math & Phys, Phys Dept, Ljubljana 1000, Slovenia..
    Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 123, no 25, article id 254101Article in journal (Refereed)
    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.

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