Summary
International Symposium on Nonlinear Theory and Its Applications
2015
Session Number:A2L-E
Session:
Number:A2L-E-1
A Probabilistic Cellular Array Model of Dissipative Wave Systems
Shohei Hamada, Atsushi Setsuie, Hisato Fujisaka, Takeshi Kamio,
pp.73-76
Publication Date:2015/12/1
Online ISSN:2188-5079
Summary:
In this paper, we propose a probabilistic cellular array which is a model of classical wave systems with dissipation. We assume particles moving from a cell to an adjacent cell of the cellular array for a unit time step. We prove analytically that the probability distribution of the particles in terms of their location satisfies the discretized classical wave equation. We also present numerically that the distribution meets the solution of the classical wave equation. If the wave functions of relativistic massless quantum particles and of electrons propagating on graphene are planar waves, the proposed cellular array is a model of these quantum systems. That is, the cellular array can be a stochastic quantization of the quantum systems.