Physical Versus Mathematical Billiards: From Regular Dynamics to Chaos and Back

Math Physics Seminar
Monday, April 8, 2019 - 10:00am for 1 hour (actually 50 minutes)
Skiles 005
L.A.Bunimovich – School of Mathematics, Georgia Tech –
Federico Bonetto

Please Note: Unusual time.

In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard sphere moves in the same billiard table, virtually anything may happen. Namely a non-chaotic billiard may become chaotic and vice versa. Moreover, both these transitions may occur softly, i.e. for any (arbitrarily small) positive value of the radius of a physical particle, as well as by a ”hard” transition when radius of the physical particle must exceed some critical strictly positive value. Such transitions may change a phase portrait of a mathematical billiard locally as well as completely (globally). These results are somewhat unexpected because for all standard examples of billiards their dynamics remains absolutely the same after transition from a point particle to a finite size (”physical”) particle. Moreover we show that a character of dynamics may change several times when the size of the particle is increasing. This approach already demonstrated a sensational result that quantum system could be more chaotic than its classical counterpart.