From integrability to chaos in quantum Liouvillians

Rubio-García, Álvaro; Molina, Rafael A.; Dukelsky, J.

doi:10.21468/scipostphyscore.5.2.026

Cited by 19 publications

(6 citation statements)

References 47 publications

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“…The advantage of this approach is that the quantum master equation is expressed only in terms of the system degrees of freedom, which facilitates its solution. In recent times, there has been a renewed interest in different aspects of the Liouvillian dynamics, especially in random systems [7][8][9][10][11][12][13][14][15][16], including the study of the spectrum [7,10,11,14], with the aim to extending the Bohigas-Giannoni-Schmit conjecture [17] to dissipative quantum systems [18][19][20], the characterization of the late-time dynamics [8][9][10]15] towards a steady state [10,16,21] or the robustness of dissipative quantum chaotic features [22].…”

Section: Discussionmentioning

confidence: 99%

Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

García-García¹,

Sá²,

Verbaarschot³

et al. 2022

Preprint

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We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, N fermions with a q-body interaction of infinite range, coupled to a Markovian environment.Close to the steady state, the real-time Lindbladian dynamics of this system at infinite temperature is identical to the near-zero-temperature dynamics in Euclidean time of a two-site non-Hermitian SYK with inter-site coupling whose gravity dual has been recently related to wormhole configurations. We show that the saddle-point equations in the real-time formulation are identical to those in Euclidean time. Indeed, an explicit calculation of Green's functions at low temperature, numerical for q = 4 and analytical for q = 2 and large q, illustrates this equivalence. Only for very strong coupling does the decay rate approach the linear dependence on the coupling characteristic of a dissipation-driven approach to the steady state. For q > 2, we identify a potential gravity dual of the real-time dissipative SYK model: a double-trumpet configuration in a near-de Sitter space in two dimensions with matter. This configuration, which we term a Keldysh wormhole, is responsible for a finite decay rate even in the absence of coupling to the environment.

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Section: Discussionmentioning

confidence: 99%

Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

García-García¹,

Sá²,

Verbaarschot³

et al. 2022

Preprint

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“…Examples include localisation in 2D random Schrödinger operators [7], dissipative quantum systems [8], random neural networks [9], quantum field theory with a quark chemical potential [10], the 3D Anderson model with disorder [11], and beyond physics in the adjacency matrix of directed complex networks [12] or ecology [13]. In particular, open chaotic quantum system have seen much activity recently, where the effect of integrability versus chaos is studied in spin chains [14][15][16] or the kicked rotor [17]. Apart from these applications, the 2D Coulomb gas (2DCG) is fascinating in its own right as a statistical mechanics problem, cf.…”

Section: Introductionmentioning

confidence: 99%

Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

2022

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A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2 × 2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β eff (β ) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β = 0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β = 1.4 and β = 2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.

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“…Because of the growing interest in non-hermitian physics, some of these properties have been generalized for non-hermitian Hamiltonians with complex eigenvalues to understand chaos or lack thereof 61,65,66 . Specifically, level spacing statistics and generalized complex spacing ratio have been calculated for open systems with the Lindbladian approach [67][68][69][70] , non-hermitian interacting disordered 61,[71][72][73] and quasiperiodic 62 systems. The complex spacing ratio has also been calculated for non-hermitian Dirac operators 74 , dissipative quantum circuits 75 , and noninteracting, non-hermitian disordered models in higher dimensions 76,77 .…”

Section: Introductionmentioning

confidence: 99%

Spectral Properties of Disordered Interacting Non-Hermitian Systems

Ghosh¹,

Gupta²,

Kulkarni³

2022

Preprint

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Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.

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From integrability to chaos in quantum Liouvillians

Cited by 19 publications

References 47 publications

Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

Spectral Properties of Disordered Interacting Non-Hermitian Systems

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