Exact formula for currents in strongly pumped diffusive systems

TL;DR

This paper derives an exact formula for probability currents in mesoscopic systems driven by nonadiabatic external parameter variations, revealing conditions for current rectification and the no-pumping theorem.

Contribution

It provides a new exact formula for currents in strongly pumped diffusive systems and clarifies the conditions needed for current rectification.

Findings

Derived an exact probability current formula for nonadiabatic driving

Established a no-pumping theorem for systems with detailed balance

Showed that broken spatial symmetry is necessary for current rectification

Abstract

We analyze a generic model of mesoscopic machines driven by the nonadiabatic variation of external parameters. We derive a formula for the probability current; as a consequence we obtain a no-pumping theorem for cyclic processes satisfying detailed balance and demonstrate that the rectification of current requires broken spatial symmetry.