Scaling crossovers in activated escape of nonequilibrium systems: a resonantly driven oscillator

TL;DR

This paper investigates the scaling behavior of metastable decay rates in a nonlinear, resonantly driven oscillator, revealing different scaling regimes and a novel exponent beyond the bifurcation point through numerical analysis.

Contribution

It establishes the parameter ranges for different scaling behaviors and uncovers a new decay rate scaling exponent in a driven oscillator system.

Findings

Scaling exponents of 1 and 3/2 depending on damping

Extended range of the 3/2 exponent beyond the bifurcation

Discovery of a new scaling exponent approximately 1.3

Abstract

The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. Our numerical calculations, based on the the instanton method allow the mapping of the entire parameter range of bi-stability. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then were it would be expected to hold as a result of an over-damped soft mode. We also uncover a new scaling behavior with exponent of $\approx$ 1.3 which extends, numerically, beyond the close vicinity of the bifurcation point.