Fermi acceleration and scaling properties of a time dependent oval billiard

Leonel, Edson D.; Oliveira, Diego F. M.; Loskutov, A. Yu.

doi:10.1063/1.3227740

Cited by 41 publications

(44 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As was found by dynamical approach, this conjecture is valid for the Lorentz gas [15], for Bunimovich' stadium [16], annular billiards [17,18] and for a family of oval billiards [19]. Lately, using the theory of dynamical systems Fermi acceleration in non-autonomous billiard-like systems has been investigated [20,21].…”

Section: Introductionmentioning

confidence: 59%

Separation of particles in time-dependent focusing billiards

Loskutov

Ryabov

Leonel

2010

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWe consider a family of stadium-like billiards with time-dependent boundaries. Two different cases of time dependence are studied: (i) the fixed boundary approximation and (ii) the exact model which takes into account the motion of the boundary. It is shown that when the billiards possess strong chaotic properties, the sequence of their boundary perturbations is the Fermi acceleration phenomenon which is three times larger than in the case of the fixed boundary approximation. However, weak mixing in such billiards leads to particle separation. Depending on the initial velocity three different things occur: (i) the particle ensemble may accelerate; (ii) the average velocity may stay constant or (iii) it may even decrease.

show abstract

Section: Introductionmentioning

confidence: 59%

Separation of particles in time-dependent focusing billiards

Loskutov

Ryabov

Leonel

2010

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…This conjecture was confirmed in many models [24][25][26]. Recently, however, [27] a specific perturbation in the boundary of an integrable elliptical billiard led to the observation of a tunable FA.…”

mentioning

confidence: 74%

Suppressing Fermi Acceleration in a Driven Elliptical Billiard

Leonel

Bunimovich

2010

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

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. Here we show that inelastic collisions suppress Fermi acceleration in a driven elliptical-like billiard. This suppression is yet another indication that Fermi acceleration is not a structurally stable phenomenon. DOI: 10.1103/PhysRevLett.104.224101 PACS numbers: 05.45.Pq, 05.45.Tp Fermi acceleration (FA) is a phenomenon that occurs when a classical particle acquires unlimited energy upon collisions with a heavy and moving wall. The original idea is due to Fermi [1] who assumed that the enormous energy of the cosmic particles comes from interactions with moving magnetic clouds. After that many different 1D Fermi accelerator models were studied [2][3][4][5]. Basically they are composed of a classical particle which experiences collisions with a moving wall. A source of returning for a next collision can be a fixed wall [3,4], a gravitational field [5], or both [6]. A simple generalization to 2D is to consider the dynamics of the particle inside a billiard domain that, depending on the shape of the boundary, demonstrates regular [7], mixed [8], or fully chaotic dynamics [9]. Applications of billiards to physical problems include superconducting [10] and confinement of electrons in semiconductors by electric potentials [11,12], ultracold atoms trapped in a laser potential [13][14][15][16], mesoscopic quantum dots [17], reflection of light from mirrors [18], waveguides [19,20], and microwave billiards [21,22].If the boundary is time dependent, the LoskutovRyabov-Akinshin (LRA) conjecture [23] claims that chaotic dynamics for a billiard with the static boundary is a sufficient condition to produce FA if a time perturbation of the boundary is introduced. This conjecture was confirmed in many models [24][25][26]. Recently, however, [27] a specific perturbation in the boundary of an integrable elliptical billiard led to the observation of a tunable FA. The result discussed in [27] was a break of two paradigms: (i) it was expected [28] that the elliptical billiard, which is integrable for static boundary and therefore demonstrates the most regular dynamics, does not exhibit FA; and (ii) since the static version of the elliptical billiard does not have chaotic dynamics, then the LRA conjecture [23] should be extended.In this Letter we show that the mechanism which produces FA in the time-dependent elliptical-like billiard can be broken by nonelastic collisions. Since the destruction is observed for very small dissipation, one can conjecture that FA is not a structurally stable phenomenon. We consider the dynamics of an ensemble of noninteracting particles in a time-dependent elliptical-like billiard. Our results show that initial conditions chosen along the separatrix curve of the billiard with a static boundary lead the particle to exhibit FA. Thus the LRA...

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Fermi acceleration and scaling properties of a time dependent oval billiard

Cited by 41 publications

References 27 publications

Separation of particles in time-dependent focusing billiards

Separation of particles in time-dependent focusing billiards

Suppressing Fermi Acceleration in a Driven Elliptical Billiard

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

Contact Info

Product

Resources

About