Skip to main content
Article thumbnail
Location of Repository

MULTI DIMENSIONAL BILLIARD-LIKE POTENTIALS

By n.n.

Abstract

The motion of a point particle travelling with a constant speed inside a region D ⊂ Rd, d ≥ 2, undergoing elastic collisions at the regions’s boundary, is known as the billiard problem. Since the days of Boltzmann, scientists have been using various billiard models to approximate the motion in systems with steep potentials (e.g. for studying classical molecular dynamics, the motion of a charged particle and cold atom’s motion in dark optical traps). In this research we develop methodologies for examining the validity and accuracy of this approximation. We consider families of smooth billiard-like potentials Vɛ, that, in the limit ɛ → 0, become singular hard-wall potentials of multi-dimensional billiards. On one hand, we provide natural conditions on these families that insure that regular reflections of the billiards are approached by their smooth trajectories. This gives a tool to understand propertie

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.9210
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.wisdom.weizmann.ac.... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.