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 Nelin. Dinam., 2010, Volume 6, Number 3, Pages 573–604 (Mi nd26)

Billiards with time-dependent boundaries and some their properties

A. Yu. Loskutova, A. B. Ryabovb, A. K. Krasnovaa, O. A. Chichiginaa

a M. V. Lomonosov Moscow State University, Faculty of Physics
b University of Oldenburg

Abstract: Classical systems of statistical mechanics — billiards of different geometry the boundaries of which are pertirbed in time — are considered. Dynamics of particles in such billiards and their statistical properties are described. Fermi acceleration which appears in consequence of the boundary oscillations in billiards of arbitrary shapes is investigated. Main attention is given on the analysis of Lorentz gas with stochastically oscillating scatterers and billiards in the form of stadium with periodically perturbed boundary. It is shown that as a result of Fermi acceleration, superdiffusion in the Lorentz gas takes place. It is found that if the shape of the stadium-type billiard is close to rectangular, then the boundary oscillations lead to a new phenomenon — separation of particles by their velocities, when the particle ensemble with high initial velocities is on averaged accelerated, while for particles with relatively low velocities the acceleration is not observed.

Keywords: billiards, Lorentz gas, superdiffusion, Fermi acceleration, dynamical chaos.

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UDC: 531.19, 517.938
MSC: 37D50, 82C05

Citation: A. Yu. Loskutov, A. B. Ryabov, A. K. Krasnova, O. A. Chichigina, “Billiards with time-dependent boundaries and some their properties”, Nelin. Dinam., 6:3 (2010), 573–604

Citation in format AMSBIB
\Bibitem{LosRyaKra10} \by A.~Yu.~Loskutov, A.~B.~Ryabov, A.~K.~Krasnova, O.~A.~Chichigina \paper Billiards with time-dependent boundaries and some their properties \jour Nelin. Dinam. \yr 2010 \vol 6 \issue 3 \pages 573--604 \mathnet{http://mi.mathnet.ru/nd26} \elib{http://elibrary.ru/item.asp?id=15223029} 

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This publication is cited in the following articles:
1. Krasnova A.K., Chichigina O.A., “Fermi Acceleration as a Possible Mechanism of Rapid Diffusion of Gold Clusters on Graphite”, Mosc. Univ. Phys. Bull., 67:1 (2012), 48–53
2. Dubinov A.E., Saikov S.K., Senilov L.A., “Model of the Stabilized Distribution Function for Oscillating Electrons in a Hollow Cathode”, Tech. Phys., 57:9 (2012), 1199–1203
3. Akhmadjanov T., Rakhimov E., Otajanov D., “Particle Dynamics in Corrugated Rectangular Billiard”, Nanosyst.-Phys. Chem. Math., 6:2, SI (2015), 262–267
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