Quantum Brownian motion under rapid periodic forcing

TL;DR

This paper investigates the steady state of a quantum Brownian particle under rapid periodic forcing, revealing an effective static potential with quantum dissipative effects, especially significant at intermediate damping levels.

Contribution

It introduces a method to analyze quantum Brownian motion with rapid periodic forcing, deriving an exact quantum dissipative potential contribution.

Findings

Quantum dissipative potential $V_{QD}$ is exactly evaluated for Ohmic baths.

$V_{QD}$ significantly influences the system at intermediate damping.

The effective static potential includes quantum effects beyond classical predictions.

Abstract

We study the steady state behaviour of a confined quantum Brownian particle subjected to a space-dependent, rapidly oscillating time-periodic force. To leading order in the period of driving, the result of the oscillating force is an effective static potential which has a quantum dissipative contribution, $V_{QD}$, which adds on to the classical result. This is shown using a coherent state representation of bath oscillators. $V_{QD}$ is evaluated exactly in the case of an Ohmic dissipation bath. It is strongest for intermediate values of the damping, where it can have pronounced effects.