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 an another measure.Introduction. -Classically chaotic quantum systems can be considered as the simplest systems exhibiting apparently time-irreversible behavior [1], and their quantum counterparts can also be the simplest systems realizing quantum irreversibility.Various examples of phenomena indicating evolution toward irreversibility, such as normal diffusion [2, 3], energy dissipation [4], energy spreading [5] and so on have been presented. Moreover, by coupling with a proper classically chaotic quantum system as a "quantum noise source", we can make a quantum system work as a quantum damper [6].However, quantum mechanical properties due to the quantum uncertainty principle prevent a quantum system from becoming irreversible in the same sense as its classical counterpart [2,3]. Indeed unbounded chaotic diffusion of a classical system is inhibited in its quantum counterpart. But if such systems are coupled even at classically negligible coupling strength, the diffusive motion exactly mimicking classical unbounded diffusion is recovered [7]. Such diffusive motion exhibits characteristics of

A very weakly coupled linear oscillator is proposed as a detector for observing timeirreversible 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 N 2 in the case of full superposition.

Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical wavepacket propagation. Some phenomenological formula of the dynamical localization length valid for wide range of control parameters are proposed for both SM and AM. For SM the formula completely agree with the experimentally established formula, and for AM the presence of a new regime of localization is confirmed. These formula can be derived by the self-consistent mean-field theory of Anderson localization on the basis of a new hypothesis for cut-off length. Transient diffusion in the large limit of the localization length is also discussed.

Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of critical phenomena, which depends on the number of frequency component M , is demonstrated. Diffusion exponents agree with theoretical prediction for the transition, but the critical exponent of the localization length deviates from it with increase in the M . The critical power ǫc of the normalized perturbation at the transition point remarkably decreases as ǫc ∼ (M − 1) −1 .

A linear oscillator very weakly coupled with the object quantum system is proposed as a detector measuring the lifetime of irreversibility exhibited by the system, and classically chaotic coupled kicked rotors are examined as ideal examples. The lifetime increases drastically in close correlation with the enhancement of entanglement entropy(EE) between the kicked rotors. In the transition regime to the full entanglement, the EE of individual eigenstates fluctuates anomalously, and the lifetime also fluctuates in correlation with the EE. In the fully entangled regime the fluctuation disappear, but the lifetime is not yet unique but increases in proportion to the number of superposed eigenstates and is proportional to the square of Hilbert space dimension in the full superposition.