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Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

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 $α$-stable Lévy distributions is considered as noise source, with varying stability index $α$ and asymmetry parameter $β$. 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 $α$ and $β$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction.