Dynamics of two interacting particles in classical billiards

Abstract

The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily constructed for this general system, which greatly simplifies calculations. As a particular example, we consider two identical particles interacting through a screened Coulomb potential in a one-dimensional billiard. We find that the screening plays an important role in the dynamical behavior of the system and only in the limit of vanishing screening length can the particles be considered as bouncing balls. For more general screening and energy values, the system presents strong non-integrability with resonant islands of stability.

REVTEX manuscript, 4 figures (1 ps + 3 gif, Postscript versions available upon request). Also available at http://www.phy.ohiou.edu/~ulloa/ulloa.html

Cited by in corpus (9)

• Statistics of the Coulomb blockade peak spacings of a silicon quantum dot
• Liquid-Solid Phase Transition of the System with Two particles in a Rectangular Box
• Origin of chaos in soft interactions and signatures of nonergodicity
• Gauss map and Lyapunov exponents of interacting particles in a billiard
• Electron interactions, classical integrability, and level statistics in quantum dots
• Billiards in magnetic fields: A molecular dynamics approach
• Interaction-induced chaos in a two-electron quantum-dot system
• Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard
• Chaotic properties of Coulomb-interacting circular billiards