Exponential Fermi acceleration in general time-dependent billiards

Batistić, Benjamin

doi:10.1103/physreve.90.032909

Cited by 23 publications

(35 citation statements)

References 38 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%

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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%

“…Time-dependent billiards (billiards with boundaries in motion) in particular can be found in a wide range of applications: KAM theory [2][3][4], one-body dissipation in nuclear dynamics [5], Fermi acceleration [2,3,[6][7][8][9][10][11][12], and adiabatic energy diffusion [13,14], for example.…”

Section: Introductionmentioning

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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“…The physics behind the unlimited energy growth is understood and is mainly related to the diffusion of velocities as a function of time [9][10][11][12]. Different regimes of growth are related to different shapes of the speed distribution function.…”

Section: Introductionmentioning

confidence: 99%

Dynamical thermalization in time-dependent billiards

Hansen

Ciro

Caldas

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds ensemble, namely, diffusion plateau, normal growth/exponential decay and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Further, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space towards a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.

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Exponential Fermi acceleration in general time-dependent billiards

Cited by 23 publications

References 38 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

Dynamical thermalization in time-dependent billiards

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