Quantum-classical correspondence in the vicinity of periodic orbits

Kumari, Meenu; Ghose, Shohini

doi:10.1103/physreve.97.052209

Cited by 18 publications

(14 citation statements)

References 28 publications

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“…The quantum kicked top (QKT) is a multiqubit, timeperiodic spin system whose classical counterpart exhibits a plethora of interesting features, such as a mixed phase space, bifurcations, and chaos [52,56]. The QKT Hamiltonian is…”

Section: Entanglement In the Qktmentioning

confidence: 99%

“…We first discuss the deep quantum regime where j is very small. In previous work [56], we presented criteria for determining the magnitude of the quantum number j at which quantum-classical correspondence will be observed near classical periodic orbits. The criteria require that the SCSs centered on all the points in a periodic orbit be almost orthogonal to each other (overlap of order roughly less than 10 −10 ) in order to observe a correspondence between the classical and the quantum dynamics near the periodic orbits on time scales sufficiently long compared to the dynamics.…”

Section: Entanglement In the Qktmentioning

confidence: 99%

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Untangling entanglement and chaos

Kumari

Ghose

2019

Phys. Rev. A

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We present a method to calculate an upper bound on the generation of entanglement in any spin system using the Fannes-Audenaert inequality for the von Neumann entropy. Our method not only is useful for efficiently estimating entanglement, but also shows that entanglement generation depends on the distance of the quantum states of the system from corresponding minimum-uncertainty spin coherent states (SCSs). We illustrate our method using a quantum kicked top model, and show that our upper bound is a very good estimator for entanglement generated in both regular and chaotic regions. In a deep quantum regime, the upper bound on entanglement can be high in both regular and chaotic regions, while in the semiclassical regime, the bound is higher in chaotic regions where the quantum states diverge from the corresponding SCSs. Our analysis thus explains previous studies and clarifies the relationship between chaos and entanglement.

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Section: Entanglement In the Qktmentioning

confidence: 99%

Section: Entanglement In the Qktmentioning

confidence: 99%

Untangling entanglement and chaos

Kumari

Ghose

2019

Phys. Rev. A

Self Cite

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“…Therefore this model is an important area of research [9,33,42,52] for the study of entanglement [37,24,45,34,4,60] and its relationship to classical dynamics [57], sign of bifurcations on different quantum correlation measures [9], quantum classical transition with respect to periodic trajectories [33] and the behavior of entropy in the transition to chaos citezs. Measure of quantum correlations is strongly correlated with the qualitative nature of classical phase space, whether it is regular or chaotic [9,52,37,3,41,20,62].…”

Section: á Fülöpmentioning

confidence: 99%

Statistical complexity of the kicked top model considering chaos

Fülöp

2020

Acta Universitatis Sapientiae, Informatica

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The concept of the statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allow us to understand this driven dynamical system by the probability distribution in phase space to make distinguish among the regular, random and structural complexity on finite simulation. We present the dependence of the kicked top and kicked rotor model through the strength excitation in the framework of statistical complexity.

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“…More recently bipartite EE as a signature of chaos was studied in the quantum kicked top (QKT) modelled as a multi-spin system [22][23][24][25][26], without the need for an external environment. In comparison with the Zurek and Paz model, one side of the bipartite system would serve analogously as the harmonic oscillator, whilst the rest of the system as the bath.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos and entanglement in ergodic and nonergodic systems

2019

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We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and non-ergodic systems. In particular we look at the quantum kicked top and kicked rotor as multi-spin systems, and investigate the single spin EE which characterizes bipartite entanglement of this spin with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems, and local chaos in non-ergodic systems. In particular, we show that EE can be maximised even when systems are highly non-ergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analogue of Kolmogorov-Arnol'd-Moser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.

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Quantum-classical correspondence in the vicinity of periodic orbits

Cited by 18 publications

References 28 publications

Untangling entanglement and chaos

Untangling entanglement and chaos

Statistical complexity of the kicked top model considering chaos

Quantum chaos and entanglement in ergodic and nonergodic systems

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