Effects of L\'evy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

TL;DR

This study explores how non-Gaussian Le9vy noise influences soliton dynamics and switching times in long Josephson junctions, revealing non-monotonic behaviors linked to soliton density and noise parameters.

Contribution

It introduces a comprehensive numerical analysis of Le9vy noise effects on soliton behavior and switching dynamics in Josephson junctions, highlighting novel non-monotonic phenomena.

Findings

Mean switching time is independent of device length beyond a critical size.

Total mean soliton density correlates with the potential difference across the junction.

Non-monotonic behaviors such as stochastic resonance and noise-enhanced stability are observed.

Abstract

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is directly related to the mean density of solitons which move into or from the washboard potential minimum corresponding to the initial superconductive state. Moreover, we observe: (i) a connection between the total mean soliton density and the mean potential difference across the junction; (ii) an inverse behavior of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidences of non-monotonic behaviors, such as stochastic resonant activation and noise enhanced stability, of MST versus the driving frequency and noise intensity for different values of $\alpha$ and $\beta$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction.