EVENT DETAILS AND ABSTRACT

Title: Big islands in dispersing billiard like potentials.
Speaker: Prof. Vered Rom-Kedar
Speaker Info: Weizmann Institute (Visiting U.Chicago)
Brief Description:
Special Note: The talk by W. Pesch that was scheduled for this day, unfortunately, has to be cancelled for now.
Abstract:

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.

The work is in collaboration with Dr. Dmitry Turaev.