Intrinsic ratchets: A Hamiltonian approach

TL;DR

This paper develops a Hamiltonian-based nonlinear Langevin equation to describe asymmetric Brownian particles acting as ratchets, revealing how their drift velocity depends on external force characteristics and particle asymmetry.

Contribution

It introduces a microscopically derived nonlinear Langevin equation beyond the weak coupling limit for asymmetric particles, enhancing understanding of ratchet mechanisms.

Findings

Drift velocity is quadratic in external force amplitude.

Maximum drift velocity is independent of particle mass.

Drift increases with decreasing force frequency and correlation time.

Abstract

An asymmetric Brownian particle subjected to an external time-dependent force may acquire a net drift velocity, and thus operate as a motor or ratchet, even if the external force is represented by an unbiased time-periodic function or by a zero-centered noise. For an adequate description of such ratchets, a conventional Langevin equation linear in the particle's velocity is insufficient, and one needs to take into account the first nonlinear correction to the dissipation force which emerges beyond the weak coupling limit. We derived microscopically the relevant nonlinear Langevin equation by extending the standard projection operation technique beyond the weak coupling limit. The particle is modeled as a rigid cluster of atoms and its asymmetry may be geometrical, compositional (when a cluster is composed of atoms of different types), or due to a combination of both factors. The drift velocity is quadratic in the external force's amplitude and increases with decreasing the force's frequency (for a periodic force) and inverse correlation time (for a fluctuating force). The maximum value of the drift velocity is independent on the particle's mass and achieved in the adiabatic limit, i.e. for an infinitely slow change of the external field.