Classical to quantum correspondence in dissipative directed transport

Carlo, Gabriel G.; Rivas, Alejandro Mariano Fidel; Spina, M E

doi:10.1103/physreve.92.052907

Cited by 7 publications

(15 citation statements)

References 43 publications

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“…We know from a previous work [20] that even for the already similarly behaved chaotic cases one needs to smooth out classical fluctuations in order to recover a quantum-like spectrum. This would put on an equal footing the spectra for different regions of parameter space in terms of their classical-quantum correspondence.…”

Section: Phase Space Representation Of the Asymptotic Eigenstatesmentioning

confidence: 99%

“…Then we turn to study complementary quantities. In this Section we look at the properties of the spectra of the Perron-Frobenius operators and the quantum superoperators [20]. For that we define the average distance between the classical and the quantum spectra ∆ q−c as the average of the euclidean distances in the complex plane between the eigenvalues λ that are nearest neighbours from both spectra.…”

Section: Spectral Correspondencementioning

confidence: 99%

“…In order to get rid of redundancies and "ghost images" derived essentially from the cylindrical topology of our phase space, we use a method that has been developed by Argüelles and Dittrich [29] (for more details on this calculation we refer to [20]). A convenient measure to compare both distributions is the overlap.…”

Section: Phase Space Representation Of the Asymptotic Eigenstatesmentioning

confidence: 99%

“…The quantum counterparts of these structures (QISSs) [18,19] have proven to be very well approximated by means of a thermal coarse graining of the classical dynamical equations (i.e., adding thermal noise of the order of eff ) in representative cases. Taking into account these examples, it was recently found [20] that the Perron-Frobenius operators associated with the classical evolution with thermal noise and the quantum superoperators without it show very similar spectra. It deserves noticing that the study of Perron-Frobenius operators in the Ulam approximation is very useful in open systems theory [21] In a recent publication a semiclassical approach has been taken into account [22].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we already know [18] that chaotic limit sets provide a quite deal of mixing with no need of noise, making uniformity unexpected. On the other hand, even for the chaotic case the thermal coarse graining is necessary to smooth out the classical fluctuations not present in the quantum version and in order to make both spectra agree [20]. To clarify this we explore the morphology of the eigenvectors associated with the equilibrium eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

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Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

Carlo¹,

Ermann²,

Rivas³

et al. 2016

Phys. Rev. E

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We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite eff values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size eff and the quantum ones without it, is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.

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Section: Phase Space Representation Of the Asymptotic Eigenstatesmentioning

confidence: 99%

Section: Spectral Correspondencementioning

confidence: 99%

Section: Phase Space Representation Of the Asymptotic Eigenstatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

Carlo¹,

Ermann²,

Rivas³

et al. 2016

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics

Kullig

Wiersig

2016

New J. Phys.

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In optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical modes appear in non-orthogonal pairs, where both modes copropagate in a preferred sense of rotation, i.e. the modes exhibit a finite chirality. Full asymmetry in the backscattering results in a non-Hermitian degeneracy (exceptional point) where the deviation from closed system evolution is strongest. We study the effects of asymmetric backscattering in ray dynamics. For this purpose, we construct a finite approximation of the Frobenius-Perron operator for deformed microdisk cavities, which describes the dynamics of intensities in phase space. Eigenstates of the Frobenius-Perron operator show nice analogies to optical modes: they come in non-orthogonal copropagating pairs and have a finite chirality. We introduce a new cavity system with a smooth asymmetric boundary deformation where we demonstrate our results and we illustrate the main aspects with the help of a simple analytically solvable 1D model.

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Identification of two mechanisms for current production in a biharmonic flashing electron ratchet

et al. 2016

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Ratchets rectify the motion of randomly moving particles, which are driven by isotropic sources of energy such as thermal and chemical energy, without applying a net, time-averaged force between source and drain. This paper describes the behavior of a damped electron, modeled by a quantum Lindblad master equation, within a flashing ratchet (a one-dimensional potential that oscillates between a flat surface and a periodic asymmetric surface). By examining the complete space of all biharmonic potential shapes and a large range of oscillation frequencies, two modes of ratchet operation, differentiated by their oscillation frequencies (relative to the rate of electron relaxation), are identified. Slow-oscillating, strong friction ratchets operate by a classical, overdamped mechanism. In fast-oscillating, weak friction ratchets, current is primarily produced when the frequency of the oscillating potential is resonant with the beating of the electron wave function in the potential well. The shape of the ratchet potential determines the direction of the current (and, in some cases, straightforwardly accounts for current reversals), but the maximum achievable current at any shape is controlled by the degree of friction applied to the electron.

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Classical to quantum correspondence in dissipative directed transport

Cited by 7 publications

References 43 publications

Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics

Identification of two mechanisms for current production in a biharmonic flashing electron ratchet

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