Spectral and steady-state properties of random Liouvillians

Sá, Lucas; Ribeiro, Pedro; Prosen, Tomaž

doi:10.1088/1751-8121/ab9337

Cited by 56 publications

(41 citation statements)

References 56 publications

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“…The model described above supports nontrivial (i.e., non-fully mixed) steady states. We find that the steady-state properties are similar to those of a random Lindbladian with non-Hermitian jump operators [20]. This is an important result as it corroborates that the properties of ρ SS of non-trivial generic quantum dynamical processes are solely determined by universality arguments.…”

Section: B Steady-state Propertiessupporting

confidence: 76%

“…In contrast, the steady-state properties are essentially the same as in the random Lindblad case, suggesting a high degree of universality. The steady state is not affected by the spectral transition, displaying, however, the same perturbative-to-RMT crossover regime at small dissipation, already observed for Lindbladian dynamics [20]. Finally, considering a 1D quantum dissipative circuit with only local interactions does not qualitatively change the results found in the unstructured case, pointing to a common universality class for the statistical properties of spatially unstructured random Kraus maps and local circuits.…”

Section: Introductionsupporting

confidence: 61%

“…The classical-probability-equation structure of the quantum dynamical equation resulting from perturbation theory in the degenerate subspace at small dissipation was already identified in Ref. [20] (at the level of the continuous-time classical Markov generator) and used to study the spectral gap of a random Liouvillian; however, its steady-state properties were not investigated. From these results (see also the related Refs.…”

Section: Small Dissipationmentioning

confidence: 99%

“…Following pioneering works on non-Hermitian Hamiltonians [8][9][10][11], some studies focused on structureless discrete-time quantum maps [12,13], and decoherence effects induced by a random environment [14][15][16]. Recently, the focus has shifted to continuous-time random Lindblad dynamics of Markovian open quantum systems [17][18][19][20][21]. These efforts led to a thorough numerical characterization of the spectral support, the spectral density, spectral gaps, and steady states, complemented by analytical calculations based on perturbative arguments and non-Hermitian RMT.…”

Section: Introductionmentioning

confidence: 99%

“…One of the most pressing is whether the universal nature of the steady-state properties identified in Ref. [20] is independent of the RMT ensemble or even from the continuousor discrete-time description of the dynamics. The goal of this paper is to tackle the aforementioned issues and make additional steps towards answering questions (i) and (ii).…”

Section: Introductionmentioning

confidence: 99%

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Spectral transitions and universal steady states in random Kraus maps and circuits

et al. 2020

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The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system), the steady state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems.

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Section: B Steady-state Propertiessupporting

confidence: 76%

Section: Introductionsupporting

confidence: 61%

Section: Small Dissipationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectral transitions and universal steady states in random Kraus maps and circuits

et al. 2020

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Non-Hermitian Hamiltonian deformations in quantum mechanics

Roccati

Cornelius

et al. 2023

J. High Energ. Phys.

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The construction of exactly-solvable models has recently been advanced by considering integrable $$ T\overline{T} $$ T T ¯ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian deformations in a nonrelativistic setting, to account for the description of a large class of open quantum systems, which includes, e.g., arbitrary Markovian evolutions conditioned to the absence of quantum jumps. We relate the time evolution operator and the time-evolving density matrix in the undeformed and deformed theories in terms of integral transforms with a specific kernel. Non-Hermitian Hamiltonian deformations naturally arise in the description of energy diffusion that emerges in quantum systems from time-keeping errors in a real clock used to track time evolution. We show that the latter can be related to an inverse $$ T\overline{T} $$ T T ¯ deformation with a purely imaginary deformation parameter. In this case, the integral transforms take a particularly simple form when the initial state is a coherent Gibbs state or a thermofield double state, as we illustrate by characterizing the purity, Rényi entropies, logarithmic negativity, and the spectral form factor. As the dissipative evolution of a quantum system can be conveniently described in Liouville space, we further study the spectral properties of the Liouvillians, i.e., the dynamical generators associated with the deformed theories. As an application, we discuss the interplay between decoherence and quantum chaos in non-Hermitian deformations of random matrix Hamiltonians and the Sachdev-Ye-Kitaev model.

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Field theory of many-body Lindbladian dynamics

Thompson

Kamenev

2023

Annals of Physics

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Spectral and steady-state properties of random Liouvillians

Cited by 56 publications

References 56 publications

Spectral transitions and universal steady states in random Kraus maps and circuits

Spectral transitions and universal steady states in random Kraus maps and circuits

Non-Hermitian Hamiltonian deformations in quantum mechanics

Field theory of many-body Lindbladian dynamics

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