A Form of Active Brownian motor-like on a (nonlinear) Toda lattice

Abstract

Results are provided about the evolution of a charged Brownian particle (an “electron”) interacting with with particles or “units” placed on a one‐dimensional Toda lattice. The thermal bath is a Gaussian white noise obeying Einstein’s fluctuation‐dissipation theorem. The electron‐lattice interaction is modeled by a Coulomb pseudo‐potential. Lattice compressions create soliton excitations (dissipative solitons) that may or may not bind the electron. The electron’s eventual trajectory depends on the (noise) temperature and on the value of the Brownian damping coefficient. It also depends on the landscape displayed by the Coulomb pseudo‐potential that allows waves traveling in either direction. Hence the system operates as a drifting ratchet, a kind of active Brownian motor for the transport of particles (or charges) along or against the solitonic motion.