Minimal chaos and stochastic webs

Chernikov, A. A.; Sagdeev, R. Z.; Usikov, D. A.; Zakharov, M. N.; Zaslavsky, G. M.

doi:10.1038/326559a0

Cited by 80 publications

(46 citation statements)

References 5 publications

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“…Perturbing a simple harmonic oscillator by a plane wave whose frequency is commensurate with the oscillator frequency has been shown to rapidly excite the oscillator [17][18][19][20][21][22][23][24][25][26]. This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28].…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that the phase space of a harmonic oscillator driven by a plane wave whose angular frequency is an integer multiple of the unperturbed harmonic-oscillator frequency is threaded by a continuous stochastic web within which the motion is unstable [17][18][19][20][21][22][23][24][25][26]29]. Each stochastic web is characterized by an infinite number of circular filaments connected by 2R radial filaments.…”

Section: Semiclassical Modeling Of the Perturbed Becmentioning

confidence: 99%

“…Stochastic webs have analytically defined structures that can be determined by expanding the Hamiltonian of the driven harmonic oscillator into Bessel functions and finding the stationary points of the system [29]. The concentric ring-shaped filaments have radii given Stochastic webs are important in many branches of physics, including plasma dynamics, Tokamak fusion, quasi crystals, condensed-matter quantum devices, and analogous optical and atomic systems [17][18][19][20][21][22][23][24][25][26]29]. One reason for this interest is that the radial filaments provide chaotic pathways along which the oscillator can diffuse, thus attaining higher ρ values and gaining energy from the plane wave.…”

Section: Semiclassical Modeling Of the Perturbed Becmentioning

confidence: 99%

“…This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28]. The excitation of the oscillator is due to the resonant creation of intricate phase-space structures known as "stochastic webs" [17][18][19][20][21][22][23][24][25][26]29], which enable the oscillator to diffuse through the web filaments away from the web center, thereby gaining energy and becoming delocalized in real space.…”

Section: Introductionmentioning

confidence: 99%

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Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

2017

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We introduce and investigate a system that uses temporal resonance-induced phase-space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form weblike patterns, can by controlled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BEC's center-of-mass kinetic energy to prespecified values. Surprisingly, the strength of the atom-lattice interaction and resulting BEC heating of the center-of-mass motion is enhanced by the repulsive interatomic interactions.

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Section: Introductionmentioning

confidence: 99%

Section: Semiclassical Modeling Of the Perturbed Becmentioning

confidence: 99%

Section: Semiclassical Modeling Of the Perturbed Becmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

2017

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“…The classical Hamiltonian of the kicked harmonic oscillator [11,17] describes a harmonically trapped (in 1D, with trap frequency ν) particle of mass m, subject to a one dimensional, spatially periodic potential (wave vector k = 2π/λ, modulation depth A) which is periodically switched on and off at integer multiples of the kicking period τ :…”

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confidence: 99%

Web-Assisted Tunneling In The Kicked Harmonic Oscillator

Carvalho

Buchleitner²

2004

Phys. Rev. Lett.

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We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web-states.PACS numbers: 05.60.Gg,05.45.Mt,42.50.Vk,82.20.Xr Controlling the state and the time evolution of quantum systems is one of the central themes of current research in experimental and theoretical atomic physics, quantum optics, and mesoscopics. Tailoring wave packets in Rydberg systems [1], producing single photons on demand [2], creating coherent superpositions of macroscopic persistent-current states [3], and, most recently, the controlled production of multiparticle entanglement [4], are prominent examples of what is often coined as "quantum state engineering", such as to stress the almost perfect control we have achieved on matter on the microscopic level. Whilst many of these schemes still rely on an analysis of the quantum dynamics in terms of some unperturbed basis of the quantum system under control, it has become clear during the last decade that generic features of strongly coupled ("complex") quantum systems allow for novel and often extremely robust strategies of quantum control. In such systems, studied in much detail in the area of quantum chaos, peculiar eigenstates emerge which exhibit unexpected (and unexpectedly robust) localization properties and dynamics. Most prominent examples thereof are nondispersive wave packets in periodically driven quantum systems [5], quantum resonances [6], and quantum accelerator modes [7]. A considerable part of these "strong coupling" quantum control schemes relies on some underlying classical dynamics, which in general is mixed regularchaotic, and precisely the rich structure of a mixed classical phase space is at their very origin [8,9]. A large class of these systems follows the Kolmogorov-Arnold-Moser (KAM) scenario [10], i.e. regular phase space structures are destroyed gradually as the coupling strength is increased. Yet, there is another kind of classically chaotic dynamics, which goes under the name "non-KAM" chaos [11], where the phase space flow is fundamentally altered at arbitrarily weak perturbations. Recently, the consequences of such non-KAM transitions have been observed in electron transport in superlattices [12], where enhanced transport accross the lattice was observed, due to the sudden (non-KAM) appearence and disappearence of unbounded stochastic web-structures in classical phase space, at well-defined values of some control parameter. Hence, enhanced transport was enforced by (controlled) abrupt changes in the underlying classical phase space structure.

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