Rectification of Fluctuations in an Underdamped Ratchet

TL;DR

This paper analytically studies the motion of underdamped particles in a periodic potential with temperature oscillations, revealing a net directed current proportional to the phase lag between potential and temperature modulations.

Contribution

It provides an analytical understanding of how temperature oscillations induce directed current in underdamped particles, highlighting the role of phase lag.

Findings

Net directed current is linear in the friction constant.

Current is proportional to the sine of the phase lag between potential and temperature.

Analytical expressions describe the particle's motion under combined potential and temperature modulations.

Abstract

We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underamped particle experiences the temperature oscillation many times in its escape out of a well and in its motion along the potential, a net directed current linear in the friction constant is found. If both the potential and the temperature modulation are sinusoidal with a phase lag $\delta$, this current is proportional to $\sin \delta$.