Measuring lifetime of correspondence with classical decay of correlation in quantum chaos

Matsui, Fumihiro; Yamada, Hiroaki; Ikeda, Kensuke S.

doi:10.1209/0295-5075/113/40008

Cited by 2 publications

(13 citation statements)

References 29 publications

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“…-In the CKR the coupling parameter ǫ sensitively controls its statistical properties. If the standard map with unbounded phase space is used for each KR, the classical chaotic diffusion is recovered as ǫ is increased beyond a threshold proportional to ̵ h. In a previous paper we showed that a similar transition occurs also for bounded finite dimensional CKR and the lifetime of correspondence with classical diffusive behavior is drastically enhanced [14].…”

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confidence: 67%

“…which predicts a seemingly strange feature that the lifetime depends on M i.e., the number of eigenstates forming the initial state Ψ 0 ⟩, where Cr 14]. Equation ( 7) explains the numerical results quite well in the fully entangled regime.…”

mentioning

confidence: 77%

“…Our method is to introduce a linear oscillator "L" which is very weakly coupled with the system S and converts S's quantum motion to a Brownian motion in the homogeneously extended action space of the linear oscillator. L is represented by the angle-action canonical pair operators θ and Ĵ = −i ̵ hd dθ with the Hamiltonian ω Ĵ of the frequency ω [14].…”

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confidence: 99%

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Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors

Matsui¹,

Yamada²,

Ikeda³

2016

EPL

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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 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

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confidence: 67%

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confidence: 77%

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Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors

Matsui¹,

Yamada²,

Ikeda³

2016

EPL

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“…which is nothing more than the temporal absorption rate A τ for z = ν = (Ω − ω) in Eq. ( 6), takes the constant classical value due to the classical chaotic decay of autocorrelation function if τ is less than the "lifetime" τ L [18]:…”

Section: Operation Of the Damper A Energy Transfer Processmentioning

confidence: 99%

“…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.…”

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confidence: 99%