Title: Big islands in dispersing billiard like potentials.
Speaker: Prof. Vered Rom-Kedar
Speaker Info: Weizmann Institute (Visiting U.Chicago)
Special Note: The talk by W. Pesch that was scheduled for this day, unfortunately, has to be cancelled for now.
The behavior of a point particle traveling with a constant speed in a region, undergoing elastic collisions at the region's boundary, is known as the billiard problem. It has been suggested that proving that dispersing billiards are ergodic and mixing is a first step for substantiating the basic assumption of statistical mechanics - the ergodic hypothesis of Boltzmann. We prove that in two dimensions, the ergodicity property may be easily lost when one considers the more realistic setting by which the particles encounter a soft potential, rather then a steep wall at the boundary (even in the limit of arbitrary steep potential). In the talk I will explain the mechanism for the lose of ergodicity and the new island structures which emerge. This casts some doubts on the validity of the Boltzmann hypothesis.Date: Friday, February 4, 2000
The work is in collaboration with Dr. Dmitry Turaev.