Quantum Dynamics of Mesoscopic Driven Duffing Oscillators

TL;DR

This paper explores the quantum behavior of a mesoscopic driven Duffing oscillator, analyzing state dynamics near bifurcation points, transient processes, and transition rates with scaling laws.

Contribution

It provides a detailed quantum analysis of bifurcation phenomena in driven Duffing oscillators, including scaling behavior and transition rate characterization.

Findings

Transition rate exhibits perfect scaling with driving distance to bifurcation.

Identified two stages in the transient process: quenching and escape.

Numerically determined the scaling exponent and compared with existing results.

Abstract

We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. In terms of Wigner function, we identify the nature of state near the bifurcation point, and analyze the transient process which reveals two distinct stages of quenching and escape. The rate process in the escape stage allows us to extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point. We numerically determine the scaling exponent, compare it with existing result, and propose open questions to be resolved.