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Research of the dynamics of the ensemble average velocity in the "corrugated waveguide" system with an oscillating boundary

A. Savin, Saratov State University, Russia; D. Lyubchenko, Saratov State University, Russia


The billiard-type systems (the particle moving in the compact space with the elastic collisions with the boundaries) are traditional for theoretical physics and nonlinear dynamics. Nowadays it is known [Loskutov A., Ryabov A. // J. Stat. Phys. 2002. Vol. 108. P. 995] that in some billard systems (e.g. stadium-like) the small oscillations of the boundary lead to the appearance of a special effect called "billiard Maxwell’s Demon": the ensemble-averaged velocity of particles increases if the initial velocity is larger than some critical value and decreases othewise. This research examines an improved Tennyson - Lieberman - Lichtenberg system [A. J. Lichtenberg, M. A. Lieberman Regular and Chaotic Dynamics] with the oscillating boundary both with and without dissipation. The four-dimensional map describing the behavior of the system is obtained and numerically simulated. The "billiard Maxwell’s Demon" effect is observed for conservative system with weak oscillations and corrugation of boundary without dissipation. In the system with dissipation quick stabilization of the velocity near the critical velocity are observed.


Lyubchenko Dmitry (
Saratov State University


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