Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

Cornelius, Julien; Xu, Zhenyu; Saxena, Avadh; Chenu, Aurélia; Campo, Adolfo del

doi:10.1103/physrevlett.128.190402

Cited by 33 publications

(14 citation statements)

References 89 publications

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“…[53]. We also stress that there are already several works that have studied different aspects of the non-Hermitian SYK model: from the use of the Lindblad formalism [54,55] and the investigation of the entanglement entropy growth [56,57] and decoherence effects [58][59][60],…”

Section: Discussionmentioning

confidence: 86%

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: 86%

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 close this section by evidencing in perspective other approaches to the description of biological and neuronal systems through the quantum-like paradigm, that make use of concepts typical of non-linear dynamics and quantum chaos. Examples include: chaotic behaviour for the amplification of emergent quantum macroscopic effects [1039], dissipative driving for the enhancement of chaotic behaviour [1060] or models for long-lasting coherence in warm noisy media due to near-criticality from quantum chaos to order, discussed e.g., in FMO complexes [1061] or in descriptions of nuclear physics via random Hamiltonians [1062]. Additionally, models for the brain as a resonating biosystem in a dissipative environment [1063], connect with ideas of time crystals [1064] and synchronisation [1065], as those discussed in Section 3.2.2, providing avenues for the description of the brain in terms of out-of-equilibrium systems [1066].…”

Section: Quantum-like Paradigm and The Brainmentioning

confidence: 99%

Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications

Yago Malo,

Lepori,

Gentini

et al. 2024

Technologies

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Physics is living an era of unprecedented cross-fertilization among the different areas of science. In this perspective review, we discuss the manifold impact that state-of-the-art cold and ultracold-atomic platforms can have in fundamental and applied science through the development of platforms for quantum simulation, computation, metrology and sensing. We illustrate how the engineering of table-top experiments with atom technologies is engendering applications to understand problems in condensed matter and fundamental physics, cosmology and astrophysics, unveil foundational aspects of quantum mechanics, and advance quantum chemistry and the emerging field of quantum biology. In this journey, we take the perspective of two main approaches, i.e., creating quantum analogues and building quantum simulators, highlighting that independently of the ultimate goal of a universal quantum computer to be met, the remarkable transformative effects of these achievements remain unchanged. We wish to convey three main messages. First, this atom-based quantum technology enterprise is signing a new era in the way quantum technologies are used for fundamental science, even beyond the advancement of knowledge, which is characterised by truly cross-disciplinary research, extended interplay between theoretical and experimental thinking, and intersectoral approach. Second, quantum many-body physics is unavoidably taking center stage in frontier’s science. Third, quantum science and technology progress will have capillary impact on society, meaning this effect is not confined to isolated or highly specialized areas of knowledge, but is expected to reach and have a pervasive influence on a broad range of society aspects: while this happens, the adoption of a responsible research and innovation approach to quantum technologies is mandatory, to accompany citizens in building awareness and future scaffolding. Following on all the above reflections, this perspective review is thus aimed at scientists active or interested in interdisciplinary research, providing the reader with an overview of the current status of these wide fields of research where cold and ultracold-atomic platforms play a vital role in their description and simulation.

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“…The spectral form factor (SFF) is an efficient tool for determining the spectral properties of a system, and it is the simplest nontrivial measure of spectral correlations [61]. This dynamical quantity is the Fourier transform of the two-level correlation function and can be interpreted as the fidelity between a coherent Gibbs state [17,[62][63][64][65], |ψ β = Z −1/2 β n e −βEn/2 |n , and its time evolution, namely…”

Section: Early-time Decay Of the Sffmentioning

confidence: 99%

Analyticity constraints bound the decay of the spectral form factor

Martinez-Azcona

Chenu

2022

Quantum

Self Cite

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Quantum chaos cannot develop faster than λ≤2π/(ℏβ) for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent λ is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponentη, that we introduce to characterize the early-time decay of the SFF, is bounded as η≤π/(2ℏβ). This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.

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Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

Cited by 33 publications

References 89 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

Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications

Analyticity constraints bound the decay of the spectral form factor

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