Robust Exponential Acceleration in Time-Dependent Billiards

Gelfreich, Vassili; Rom‐Kedar, Vered; Shah, Kushal; Turaev, Dmitry

doi:10.1103/physrevlett.106.074101

Cited by 51 publications

(83 citation statements)

References 27 publications

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“…The problem is complicated for non-chaotic multi-dimensional billiards as well. Integrable billiards may prohibit [20] or allow [21] quadratic or slower Fermi acceleration, while exponential Fermi acceleration is possible for pseudo-integrable billiards [22] and billiards with multiple ergodic components [10,12,[23][24][25] with possibly mixed or pseudo-integrable dynamics.…”

Section: Fermi Accelerationmentioning

confidence: 99%

Universal energy diffusion in a quivering billiard

Demers

Jarzynski

2015

Phys. Rev. E

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We introduce and study a model of time-dependent billiard systems with billiard boundaries undergoing infinitesimal wiggling motions. The so-called quivering billiard is simple to simulate, straightforward to analyze, and is a faithful representation of time-dependent billiards in the limit of small boundary displacements. We assert that when a billiard's wall motion approaches the quivering motion, deterministic particle dynamics become inherently stochastic. Particle ensembles in a quivering billiard are shown to evolve to a universal energy distribution through an energy diffusion process, regardless of the billiard's shape or dimensionality, and as a consequence universally display Fermi acceleration. Our model resolves a known discrepancy between the one-dimensional Fermi-Ulam model and the simplified static wall approximation. We argue that the quivering limit is the true fixed wall limit of the Fermi-Ulam model.

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Section: Fermi Accelerationmentioning

confidence: 99%

Universal energy diffusion in a quivering billiard

Demers

Jarzynski

2015

Phys. Rev. E

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“…This unlimited growth of energy was denoted Fermi acceleration (FA) and is mainly associated with normal diffusion in phase space, where there is gain of kinetic energy [2]. One may find in the literature examples of FA that may present transport distinct from the normal diffusion, as exponential [3][4][5][6], ballistic [7,8] or even slower growths [9,10]. Also, interesting FA applications can be found in research areas such as plasma physics [11][12][13], astrophysics [14,15], atom-optics [16,17], and especially billiard dynamics [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Transition from normal to ballistic diffusion in a one-dimensional impact system

et al. 2018

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We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of noninteracting particles, experiencing elastic collisions with a heavy and periodically moving wall under the influence of a constant gravitational field. The dynamics lead to a mixed phase space where chaotic orbits have a free path to move along the velocity axis, presenting a normal diffusion behavior. Depending on the control parameter, one can observe the presence of featured resonances, known as accelerator modes, that lead to a ballistic growth of velocity. Through statistical and numerical analysis of the velocity of the particle, we are able to characterize a transition between the two regimes, where transport properties were used to characterize the scenario of the ballistic regime. Also, in an analysis of the probability of an orbit to reach an accelerator mode as a function of the velocity, we observe a competition between the normal and ballistic transport in the midrange velocity.

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“…In the particular focus of this work, the mechanism of FA has been noticed in the stadiumlike billiard [2,9,11,12], in the annular billiard [3,4,10], in the one-dimensional stochastic Fermi-Ulam billiard [5,6], in the elliptical billiard [7,8], in the Sinai's billiard [9,11], and in the Lorentz gas-like billiard [16]. Recent results on FA associated with the interaction of charge particles with magnetic islands or mirrors have also been reported [14,15,17,18].…”

Section: Introductionmentioning

confidence: 96%

“…In recent years, several studies have been developed in order to show dynamical properties which could contribute for inducing or suppressing Fermi acceleration (FA), which can be named as indefinite energy growth [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The Loskutov-Ryabov-Akinshin conjecture says that a chaotic regime observed in static billiards is a sufficient condition to find FA when a periodic time-dependent perturbation is added on the billiard boundaries [1].…”

Section: Introductionmentioning

confidence: 99%

Tunable Fermi acceleration in a nondissipative driven magnetic billiard

et al. 2014

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We study the effect of a constant magnetic field on the dynamics of a system that may present Fermi acceleration (FA). The model in consideration is the nondissipative annular billiard with breathing boundaries. There is a field threshold, from which the mechanism of FA can be deactivated. The presence of the magnetic field curves the particle trajectories and for some combinations of the parameters FA is totally, and nontrivially, suppressed without considering any kind of dissipation.

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Robust Exponential Acceleration in Time-Dependent Billiards

Cited by 51 publications

References 27 publications

Universal energy diffusion in a quivering billiard

Universal energy diffusion in a quivering billiard

Transition from normal to ballistic diffusion in a one-dimensional impact system

Tunable Fermi acceleration in a nondissipative driven magnetic billiard

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