title: Universal energy diffusion in a quivering billiard.
abstract: We introduce and study a model of time-dependent billiard systems with billiard boundaries undergoing infinitesimal wiggling motions. The so-called quivering billiard is simple to simulate, straightforward to analyze, and is a faithful representation of time-dependent billiards in the limit of small boundary displacements. We assert that when a billiard's wall motion approaches the quivering motion, deterministic particle dynamics become inherently stochastic. Particle ensembles in a quivering billiard are shown to evolve to a universal energy distribution through an energy diffusion process, regardless of the billiard's shape or dimensionality, and as a consequence universally display Fermi acceleration. Our model resolves a known discrepancy between the one-dimensional Fermi-Ulam model and the simplified static wall approximation. We argue that the quivering limit is the true fixed wall limit of the Fermi-Ulam model.
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Jeffery
authors.initials: J
authors.lastname: Demers
authors.affiliation: Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Christopher
authors.initials: C
authors.lastname: Jarzynski