We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived. The formula contains a correlation function that can be evaluated only from the information of uncoupled tops. Using this expression and the assumption that the correlation function decays exponentially which is plausible for chaotic tops, it is shown that the increment of the strength of chaos does not enhance the production rate of entanglement when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic. The result is confirmed by numerical experiments. The perturbative approach is also applied to a weakly chaotic region, where tori and chaotic sea coexist in the corresponding classical phase space, to reexamine a recent numerical study that suggests an intimate relationship between the linear stability of the corresponding classical trajectory and the entanglement production rate.
The production of quantum entanglement between weakly coupled mapping systems, whose classical counterparts are both strongly chaotic, is investigated. In the weak-coupling regime, it is shown that time-correlation functions of the unperturbed systems determine the entanglement production. In particular, we elucidate that the increment of the nonlinear parameter of coupled kicked tops does not accelerate the entanglement production in the strongly chaotic region. An approach to the dynamical inhibition of entanglement is suggested.
We present a unified formulation of quantum holonomy which is capable of describing all of its known varieties. The full role of non-Abelian gauge connection is elucidated. As examples, solvable models of quantum kicked spin are analyzed. They are shown to exhibit spiral holonomy, as well as Berry phase and Wilczek-Zee holonomy.This paper is dedicated to the memory of Attila Nyá.
The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated. While the Floquet operator of the map and its spectrum have a common period with respect to the perturbation strength lambda, we show an example in which none of the quasienergies nor the eigenvectors obey the same period: After a periodic increment of lambda, the quasienergy arrives at the nearest higher one, instead of the initial one, exhibiting an anholonomy, which governs another anholonomy of the eigenvectors. An application to quantum state manipulations is outlined.
We examine a parametric cycle in the N -body Lieb-Liniger model that starts from the free system and goes through Tonks-Girardeau and super-Tonks-Girardeau regimes and comes back to the free system. We show the existence of exotic quantum holonomy, whose detailed workings are analyzed with the specific sample of two-and three-body systems. The classification of eigenstates based on clustering structure naturally emerges from the analysis.
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