Environmental stability of quantum chaotic ratchets

Carlo, Gabriel G.; Ermann, Leonardo; Borondo, F.; Benito, R. M.

doi:10.1103/physreve.83.011103

Cited by 9 publications

(5 citation statements)

References 53 publications

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“…Examples of ratchet models (as they are also usually referred to) have found application in many areas of research. Here we will mention just a few, such as biology [4], nanotechnology [5], granular crystals [6], and some chemical reactions as isomerization [7]. This gives an idea of how different the fields of interest could be.…”

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confidence: 99%

Quantum parameter space of dissipative directed transport

Ermann

Carlo

2015

Phys. Rev. E

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Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of eff in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems. The idea of directed transport [1] proved to be very fruitful, and has attracted a huge interest in recent years [2] It can be very briefly defined as transport phenomena in spatial and time periodic systems which are not subject to thermal equilibrium. The current appears since all spatiotemporal symmetries leading to momentum inversion are broken [3]. Examples of ratchet models (as they are also usually referred to) have found application in many areas of research. Here we will mention just a few, such as biology [4], nanotechnology [5], granular crystals [6], and some chemical reactions as isomerization [7]. This gives an idea of how different the fields of interest could be.At the classical level, deterministic ratchets with dissipation are generally associated with an asymmetric chaotic attractor [8]. Quantum ratchets show very rich behavior [9]. In this respect we should mention that cold atoms in optical lattices have been deeply investigated from both, the theoretical and experimental points of view [10,11]. This extends also to Bose-Einstein condensates, which have been transported by means of quantum ratchet accelerators [12], where the current has no classical counterpart [13] and the energy grows ballistically [14,15]. Within this framework, a dissipative quantum ratchet interesting for cold atoms experiments has been introduced in [16]. Very recently, the parameter space of the classical counterpart of this system has been the object of a detailed study [17,18]. There it has been found that families of isoperiodic stable structures (ISSs are Lyapunov stable islands, generic in the parameter space of dissipative systems), have a very important role in the description of the currents. Subsequently, the effects of temperature have been included in the investigations leading to the determination of resistant optimal ratchet transport in its presence [19].When looking at the quantum counterparts of these * ermann@tandar.cnea.gov.ar, carlo@tandar.cnea.gov.ar structures it has recen...

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Quantum parameter space of dissipative directed transport

Ermann

Carlo

2015

Phys. Rev. E

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“…We have studied two paradigmatic systems, namely the DMKRM [14], and a generic, continuously driven DPDDS [15] We have found that we can always identify a classical chaotic attractor which corresponds to the quantum one. In general, there are no paradoxes in the quantum to classical correspondence of dissipative systems when we add Gaussian fluctuations to the classical counterparts.…”

Section: Discussionmentioning

confidence: 99%

“…This system is interesting to simulate a molecule with two stable isomers that is under the influence of a monochromatic laser field pulse, for which the term sin(x) represents the dipole coupling [15]. But it is also of general nature, and the results obtained through its study can be directly applied to many different situations, including for example many body systems [9].…”

Section: B Dpddsmentioning

confidence: 99%

“…The quantum mechanical evolution is performed by means of a modified split operator method [15,20]. In fact, we compose unitary steps given by the kinetic and potential terms of the Hamiltonian, and other purely dissipative ones.…”

Section: B Dpddsmentioning

confidence: 99%

“…In order to throw light over some of these features we study two paradigmatic systems: a dissipative modified kicked rotator map (DMKRM) which has been very fruitful in directed transport theory [14], and a dissipative periodically driven dynamical system (DPDDS) that has applications in isomerization reactions [15] and which is fundamental to support the generic nature of our ideas. We concentrate on the case of a small but finite value of the effective Planck constant eff .…”

Section: Introductionmentioning

confidence: 99%

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Classical counterparts of quantum attractors in generic dissipative systems

et al. 2017

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In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.

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