Nonlinear dynamics and quantum chaos of a family of kicked 
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-spin models

Muñoz-Arias, Manuel H.; Poggi, Pablo M.; Deutsch, Ivan

doi:10.1103/physreve.103.052212

Cited by 18 publications

(6 citation statements)

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“…As a paradigmatic model for both theoretical [7][8][9][10][11][71][72][73][74][75][76][77][78] and experimental [79][80][81][82] studies of quantum chaos, the kicked top model consists of a larger spin with total angular momentum j whose dynamics is captured by the following Hamiltonian (throughout this work, h = 1) [10,71]:…”

Section: Kicked-top Modelmentioning

confidence: 99%

“…To show this, we first introduce the scaled spin operators S a = J a /j, which behave as classical variables due to the vanishing commutators between them as j → ∞. Then, by factorizing the mean values of the products of the angular momentum operators as J a J b /j 2 = S a S b [9,78,83], it is straightforward to find that the stroboscopic map of the classical angular momentum can be written as [10]   S x (n + 1) S y (n + 1) S z (n + 1)…”

Section: Classical Kicked Topmentioning

confidence: 99%

“…To quantify the chaotic features observed in Figure 1a, we investigate the behavior of the largest Lyapunov exponent of the classical map in Equation (12). The largest Lyapunov exponent measures the rate of divergence between two infinitesimally close orbits of a dynamical system [78,84,85]. The largest Lyapunov exponent, therefore, estimates the level of chaos.…”

Section: Classical Kicked Topmentioning

confidence: 99%

“…with initial condition δS(0). Then, the largest Lyapunov exponent of the classical kicked top can be calculated as [78,88]…”

Section: Classical Kicked Topmentioning

confidence: 99%

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Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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Section: Kicked-top Modelmentioning

confidence: 99%

Section: Classical Kicked Topmentioning

confidence: 99%

Section: Classical Kicked Topmentioning

confidence: 99%

“…with initial condition δS(0). Then, the largest Lyapunov exponent of the classical kicked top can be calculated as [78,88]…”

Section: Classical Kicked Topmentioning

confidence: 99%

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Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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“…In contrast to the case of classical chaos, which is well defined as the exponential divergence of the closest orbits for initial perturbations [12,13], the definition of quantum chaos in the narrow sense remains an open question [14]. One, therefore, turns to focus on how to probe and measure the signatures of chaos in various quantum systems [1,2,[15][16][17][18][19][20][21][22]. To date, the presence of chaos in a quantum system is commonly ascertained from its spectral properties.…”

Section: Introductionmentioning

confidence: 99%

Statistics of phase space localization measures and quantum chaos in the kicked top model

Wang¹,

Robnik²

2023

Preprint

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Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi functions), we explore the characterizations of quantum chaos using the statistics of the localization measures. We consider the paradigmatic kicked top model, which shows a transition to chaos with increasing the kicking strength. We demonstrate that the distributions of the localization measures exhibit a drastic change as the system undergoes the crossover from integrability to chaos. We also show how to identify the signatures of quantum chaos from the central moments of the distributions of localization measures. Moreover, we find that the localization measures in the fully chaotic regime apparently exhibit universally the beta distribution, in agreement with previous studies in the billiard systems and the Dicke model. Our results contribute to a further understanding of quantum chaos and shed light on the usefulness of the statistics of phase space localization measures in diagnosing the presence of quantum chaos, as well as the localization properties of eigenstates in quantum chaotic systems.

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