For convenience, the billiard shape and its orientation with respect to the tensor is represented with the shaded area. b) A time evolution of E2 for three different v0 in a circularly translating - "Fermi acceleration in chaotic shape-preserving billiards."

We show, on the other hand, that if a shape of a fully chaotic time-dependent billiard is preserved then there are only three possible values of β depending solely on the rotational properties of the billiard. We study dynamical properties of an ensemble of noninteracting particles in a time-dependent elliptical-like billiard. It was recently shown [Phys. Rev. Lett. 100, 014103 (2008)] that for the nondissipative dynamics, the particle experiences unlimited energy growth.

Acceleration in billiards

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The LRA conjecture states that "chaotic dynamics of a billiard with a fixed boundary is a sufficient condition for the Fermi acceleration in the system when a boundary perturbation is introduced".

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In chaotic billiards, even if the boundary velocity is a smooth function of time, the incidence angle of a particle can be treated as a random parameter. Consequently, the normal energy growth in systems with impacts is known as Fermi acceleration mechanism.
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In the process of slow evolution, ce We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law v =nβ with respect to the number of collisions n. If a shape of a fully chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent Fiz. 116, 1781–1797 共November 1999兲 The paper is devoted to the problem of Fermi acceleration in Lorentz-type dispersing billiards whose boundaries depend on time in a certain way.

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10 Jul 2019 This allows the study of non-equilibrium dynamics such as diffusion in momentum space e.g. Fermi acceleration, or - in the case of spatially

We study the affect of different parameters that control the geometry of the billiard in this model. We consider variations of different parameters of the model and describe how the particle trajectory is The LRA conjecture states that "chaotic dynamics of a billiard with a fixed boundary is a sufficient condition for the Fermi acceleration in the system when a boundary perturbation is introduced". annular (chaotic) billiards.

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TP A.4. contains the full derivation. acceleration. In chaotic billiards, even if the boundary velocity is a smooth function of time, the incidence angle of a particle can be treated as a random parameter. Consequently, the normal energy growth in systems with impacts is known as Fermi acceleration mechanism. Recently, it has been numerically shown that Fermi acceleration exists in elliptic time-dependent billiards. Due to the Hamiltonian nature of biUiard dynamics, they can be analysed via … 2013-05-06 It is shown, that under very general conditions, a generic time-dependent billiard, for which a phase-space of corresponding static (frozen) billiards is of the mixed type, exhibits the exponential Fermi acceleration in the adiabatic limit.

25 sep. 2013 — the World Professional Billiards and Snooker Association (WPBSA) said on Monday. This is the fastest rate of acceleration in 28 months.

A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. Fiz. 116, 1781–1797 共November 1999兲 The paper is devoted to the problem of Fermi acceleration in Lorentz-type dispersing billiards whose boundaries depend on time in a certain way. Two cases of boundary oscillations are considered: the stochastic case, when a boundary changes following a random function, and a regular case with a boundary varied according to a harmonic law. We study the dynamical properties of a particle in a non-planar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane.

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