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The relation between the degree of entanglement and time scale of time-irreversible behavior is investigated for classically chaotic quantum coupled kicked rotors by comparing the entanglement entropy (EE) and the lifetime of correspondence with classical decay of correlation, which was recently introduced. Both increase on average drastically with a strong correlation when the strength of coupling between the kicked rotors exceeds a certain threshold. The EE shows an anomalously large fluctuation resembling a critical fluctuation around the threshold value of coupling strength where the entanglement sharply increases toward full entanglement. In this regime it can be shown that, although the correlation is hidden, EE and the lifetime of individual eigenfunctions also have a positive correlation that can be seen via another measure. [ABSTRACT FROM AUTHOR]

A very weakly coupled linear oscillator is proposed as a detector for observing time-irreversible characteristics of a quantum system, and it is used to measure the lifetime during which a classically chaotic quantum system shows decay of correlation. Except for a particular case where the lifetime agrees with the conventional Heisenberg time, which is proportional to the Hilbert space dimension N, it is in general much longer: the lifetime increases in proportion to the product of N and the number of superposed eigenstates, and is proportional to N2 in the case of full superposition. [ABSTRACT FROM AUTHOR]

The Stokes geometry for the propagator of the quantum Hénon map is studied in the light of recent developments of the exact WKB analysis. As the simplest possible situation the Hénon map satisfying the so-called horseshoe condition is closely analyzed, together with listing up local bifurcation patterns of the Stokes geometry. This is exactly in the same spirit as pruning theory for the classical horseshoe system, and the present paper is placed as the first step to establish pruning theory of the Stokes geometry for chaotic systems. Our analysis reveals that the birth and death of the WKB solutions caused by the Stokes phenomenon do not occur in a local but entirely global manner, reflecting topological nature encoded in the Stokes geometry. We derive an explicit general formula to enumerate the number of WKB solutions in the asymptotic region and obtain its growth rate, which is shown to be less than the topological entropy of the corresponding classical dynamics. The relations to the diffraction catastrophe integrals and one-step multiply folding maps are also discussed. [ABSTRACT FROM AUTHOR]

The instanton-noninstanton (I-NI) transition in the tunneling process, which has been numerically observed in classically nonintegrable quantum maps, can be described by a perturbation theory based on an integrable Hamiltonian renormalized so as to incorporate the integrable part of the map. The renormalized perturbation theory is successfully applied to the two quantum maps, the Hénon and standard maps. In spite of the different nature of tunneling in the two systems, the I-NI transition exhibits very common characteristics. In particular, the manifestation of I-NI transition is obviously explained by a remarkable quenching of the renormalized transition matrix element. The enhancement of tunneling probability after the transition can be understood as a sudden change of the tunneling mechanism from the instanton to quite a different mechanism supported by classical flows just outside of the stable-unstable manifolds of the saddle on the top of the potential barrier. [ABSTRACT FROM AUTHOR]

In recent years a new description has been developed for tunnelling in multi-dimensional systems based on complexified stable-unstable manifolds of periodic saddles. The complexified stable-unstable manifolds guide complex-classical tunnelling trajectories over the energetic barrier (Takahashi and Ikeda 2003 J. Phys. A: Math. Gen. 36 7953). In this paper it is claimed, based on theoretical analysis and numerical evidence, that the tunnelling mechanism due to complexified stable-unstable manifolds is associated with a characteristic plateau feature in the tunnelling spectrum. An analysis of a particular two-dimensional barrier tunnelling model shows that the plateau feature is obtained by a fully quantum-mechanical computation, and that the complex-semiclassical theory successfully reproduces this feature. Moreover, an analytical theory based upon Melnikov's method is developed and used to clarify quantitatively how the tunnelling mechanism due to the complexified stable-unstable manifolds leads to the formation of the plateau structure; in particular, it is shown that the classical action along the complexified stable manifold controls the height of the plateau. The analysis presented here is based on a particular model, but the main claims should hold for any system with multi-dimensional barrier tunnelling because of the universality of the underlying mechanism. [ABSTRACT FROM AUTHOR]