Statistical and dynamical properties of the quantum triangle map

Wang, Jiaozi; Benenti, Giuliano; Casati, Giulio; Wang, Wenge

doi:10.1088/1751-8121/ac6a93

Cited by 9 publications

(3 citation statements)

References 37 publications

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“…For systems with well-defined classical or semiclassical limits, quantum chaos refers to signatures found in the quantum domain, such as level statistics as in full random matrices [21], that indicate whether the classical system is chaotic in the sense of positive Lyapunov exponent and mixing. While this correspondence holds well for some systems with a small number of degrees of freedom, such as Sinai's billiard [1,2], it has recently been shown to be violated in triangular billiards [22] and quantum triangle maps [23]. As one moves to systems with many interacting particles, this issue gets even more complicated, since the classical limit is not always straightforward [24].…”

Section: Introductionmentioning

confidence: 99%

Chaos enhancement in large-spin chains

2023

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We study the chaotic properties of a large-spin XXZ chain with onsite disorder and a small number of excitations above the fully polarized state. We show that while the classical limit, which is reached for large spins, is chaotic, enlarging the spin suppresses quantum chaos features. We examine ways to facilitate chaos by introducing additional terms to the Hamiltonian. Interestingly, perturbations that are diagonal in the basis of product states in the zz-direction do not lead to significant enhancement of chaos, while off-diagonal perturbations restore chaoticity for large spins, so that only three excitations are required to achieve strong level repulsion and ergodic eigenstates.

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Section: Introductionmentioning

confidence: 99%

Chaos enhancement in large-spin chains

2023

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“…It also turns out that many features of the TM are still debated, starting from basic properties, such as ergodicity and mixing (see, for instance, [17,18]). It is also worth mentioning that the TM has been studied in the quantum setting to investigate which features of quantum chaos are displayed in the absence of classical exponential instability [19,20].…”

Section: Introductionmentioning

confidence: 99%

Records and Occupation Time Statistics for Area-Preserving Maps

Artuso

Oliveira

Manchein

2023

Entropy

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A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated with stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on non-compact phase space. We consider here two examples of area-preserving maps: the Chirikov–Taylor standard map and the Casati–Prosen triangle map, and we investigate transport properties, records statistics, and occupation time statistics. Our results confirm and expand known results for the standard map: when a chaotic sea is present, transport is diffusive, and records statistics and the fraction of occupation time in the positive half-axis reproduce the laws for simple symmetric random walks. In the case of the triangle map, we retrieve the previously observed anomalous transport, and we show that records statistics exhibit similar anomalies. When we investigate occupation time statistics and persistence probabilities, our numerical experiments are compatible with a generalized arcsine law and transient behavior of the dynamics.

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“…The present article is dedicated to Professor Giulio Casati on the occasion of his 80th birthday in 2022 and to Professor Felix Izrailev's 80th birthday in 2021. Not only their past, but also their recent works [31][32][33][34][35][36][37][38] continue to have an enormous impact in the developments of quantum chaos and its connections with thermalization, quantum statistical mechanics, and the quantum-classical correspondence.…”

Section: Introductionmentioning

confidence: 99%

Chaos and Thermalization in the Spin-Boson Dicke Model

Villaseñor

Pilatowsky-Cameo

Bastarrachea-Magnani

et al. 2022

Entropy

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We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called “efficient basis” over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.

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Statistical and dynamical properties of the quantum triangle map

Cited by 9 publications

References 37 publications

Chaos enhancement in large-spin chains

Chaos enhancement in large-spin chains

Records and Occupation Time Statistics for Area-Preserving Maps

Chaos and Thermalization in the Spin-Boson Dicke Model

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