Directed motion of Brownian particles with internal energy depot

TL;DR

This paper introduces a model of Brownian particles with an internal energy depot that enables directed motion in a ratchet potential, analyzing deterministic and stochastic behaviors, current reversals, and optimal noise conditions.

Contribution

The study presents a novel model combining internal energy storage with Brownian motion, exploring its dynamics and current behavior in ratchet systems, including stochastic effects and reversals.

Findings

Directed motion depends on energy supply levels.

Stochastic influences can reverse current direction.

Optimal noise intensity maximizes net current.

Abstract

A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Sect. 2 is investigated for the deterministic and stochastic particle's motion in a non-fluctuating ratchet potential. First, we discuss the attractor structure of the ratchet system by means of computer simulations. Dependent on the energy supply, we find either periodic bound attractors corresponding to localized oscillations, or one/two unbound attractors corresponding to directed movement in the ratchet potential. Considering an ensemble of particles, we show that in the deterministic case two currents into different directions can occur, which however depend on a supercritical supply of energy. Considering stochastic influences, we find the current only in one direction. We further investigate how the current reversal depends on the strength of the stochastic force and the asymmetry of the potential. We find both a critical value of the noise intensity for the onset of the current and an optimal value where the net current reaches a maximum. Eventually, the dynamics of our model is compared with other ratchet models previously suggested.