Ratchet transport for a chain of interacting charged particles

TL;DR

This paper investigates the directed transport of a chain of interacting charged particles under an alternating electric field and ratchet potential, providing analytical and numerical insights into conditions for integer and fractional chain motion.

Contribution

It introduces a detailed analysis of chain dynamics with specific ratchet potentials, deriving motion criteria and explicit transport results for the first time.

Findings

Both integer and fractional transport can occur.

Explicit transport results for double-sine and phase-modulated sine ratchets.

Derived drift criterion for chain motion.

Abstract

We study analytically and numerically the overdamped, deterministic dynamics of a chain of {\it charged}, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion for chain motion. For ratchet potentials of the form of a double-sine and a phase-modulated sine it is demonstrated that both, a so-called integer and fractional transport of the chain can occur. Explicit results for the directed chain transport for these two classes of ratchet potentials are presented.