CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoretično fiziko

Velocity dynamics in time dependent billiards

Benjamin Batistić
CAMTP, University of Maribor

Abstract: A point particle is moving freely inside a time varying domain while experiencing elastic reflections on its boundary. The energy is not conserved and can reach arbitrarily large value (Fermi acceleration). This phenomenon was originally proposed by Fermi and Ulam as the mechanism for the acceleration of high energy cosmic rays. It is a subject of intense current research worldwide. According to many numerical simulations in various billiard systems where Fermi acceleration is observed the mean velocity of an ensemble of particles follows the power law $\left<v\right>\propto n^{\beta}$, where $n$ is the number of collisions and $\beta$ is the system dependent acceleration exponent. I shall present the first theoretical derivation [1] of $\beta=1/6$ for important class of conformally breathing billiards. I shall also analyze the velocity dynamics of a single trajectory, independent of the properties of the underlying static billiard.

[1] Batistić B and Robnik M Fermi acceleration in time dependent billiards: Theory of the velocity diffusion in conformally breathing fully chaotic billiards, submitted to J. Phys. A: Math. Theor. 2011

Seminarsko predavanje bo v četrtek 14. aprila 2011 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje. Vljudno vabljeni vsi zainteresirani, tudi študenti.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --