Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors

Abstract

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

Slow heating in a quantum coupled kicked rotors system

“…As stated above, even a partly chaotic phase space is enough to have Arnold diffusion, and this fact translates in a diffusive long-term dynamics, possibly after a transient [36,5,37,38,7]. In the quantum case the behavior is different and dynamical localization can persist for a finite number of rotors [39,40,41,42,43]. Nevertheless, it disappears in the thermodynamic limit, when the number of rotors tends to infinity [39] (although it can persist in the thermodynamic limit in other systems [44,45]).…”

A quantum damper

“…As has been discussed in detail in the previous paper [19], the short saturation time means that in a single KR the number of eigenstates which are significantly connected with an eigenstate by the interaction potential ηqf ( Î) cos ωt in Eq. ( 1) is much less than N .…”

“…With the method we can map the Fourier spectral features of correlation function to the diffusion characteristics of a fictious measurement system. Applying the method to coupled quantum chaotic rotors, we found that the time scale on which the decay-able quantum correlation is maintained is proportional to N 2 dim , not N dim if a full entanglement is achieved among the quantum chaos units [18,19]. We called this "lifetime" of the decay-able correlation.…”

Interscale entanglement production in a quantum system simulating classical chaos

“…We here make some remarks on related previous studies. The long-time average of entanglement entropy in quantum chaotic systems is known to play an essential role as an indicator of chaos [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. In general, for initial wave packets belonging to a chaotic region in classical phase space, the longtime average of entanglement entropy is much larger than that of the regular case.…”