Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force

TL;DR

This study explores how quantum effects influence ratchet currents in a Brownian system driven by a biharmonic force, revealing that tunneling can either enhance or suppress current depending on barrier height and temperature.

Contribution

The paper introduces a formalism using reduced hierarchy equations in Wigner space to analyze quantum dissipative ratchet dynamics across classical and tunneling regimes, highlighting quantum suppression effects.

Findings

Quantum current exceeds classical at high barriers and low temperatures.

Tunneling enhances current in high barriers but suppresses it in low barriers.

Weak ratchet potential due to tunneling reduces net current in low barrier cases.

Abstract

We rigorously investigate the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force. In this model, we use the reduced hierarchy equations of motion in the Wigner space representation. These equations represent a generalization of the Gaussian-Markovian quantum Fokker-Planck equation introduced by Tanimura and Wolynes (1991), which was formulated to study non-Markovian and non-perturbative thermal effects at finite temperature. This formalism allows us to treat both the classical limit and the tunneling regimes, and it is helpful for identifying purely quantum mechanical effects through the time evolution of the Wigner distribution. We carried out extensive calculations of the classical and quantum currents for various temperatures, coupling strengths, and barrier heights. Our results reveal that at low temperature, while the quantum current is larger than the classical current in the case of a high barrier, the opposite is true in the case of a low barrier. We find that this behavior results from the fact that the tunneling enhances the current in the case of a high barrier, while it suppresses the current in the case of a low barrier. This is because the effect of the ratchet potential is weak in the case of a low barrier, due to the large dispersion of the distribution introduced by tunneling. This causes the spatio-temporal asymmetry, which is necessary for ratchet current, to be weak, and as a result, the net current is suppressed.