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 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**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
, where
is the number of collisions and is the system dependent
acceleration exponent.
I shall present the first theoretical derivation [1] of
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

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