Nonergodicity and localization of invariant measure for two colliding masses.
We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For nongeneric mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of π, the system is ergodic, consistent with existing rigorous results.
Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China.
Jiao
J
Wang
CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy.
Giulio
G
Casati
Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
Tomaž
T
Prosen