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

Abstract

Abstract. We numerically investigate the generation of solitons in currentbiased 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 a noise source, with varying stability index α and asymmetry parameter β. In junctions longer than a critical length, the mean switching time (MST) from the superconductive to the resistive state assumes a value independent of the device length. Here, we demonstrate that this 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 dierence across the junction; (ii) an inverse behaviour of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidence of non-monotonic behaviours, such as stochastic resonant activation and noise-enhanced stability, of the MST versus the driving frequency and noise intensity for dierent values of α and β; (iv) finally, these

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

“…The MST τ as a function of the driving frequency ω for several noise intensities γ, i 0 = 0.5, and τ d = 3, are shown in Figure 3. Moreover, the length is set to L = 20, it means a junction long enough to observe solitons formation along the string [17,81,91,120].…”

“…Specifically, we investigate the mean switching time (MST), namely, the average time the junction takes to switch from the superconducting state to the resistive regime, as a function of several parameters of system and noise source. The phase dynamics of a LJJ, analyzed within the sine-Gordon (SG) formalism [17,81,90], is characterized by a peculiar excitation, called soliton or kink [107,108], related to the penetration of a magnetic flux quantum, i.e., fluxons [109,110], generated by a supercurrent circulating around it.…”

“…The effects of a dichotomous noise source is taken into account by the term i DN (t). For the sake of understanding the exclusive effect of the dRTN source i DN (t) on the LJJ response, a thermal noise source, which effects were formerly extensively explored in the LJJ context [17,81,[119][120][121][122][123], is ignored in this model. A LJJ can be depicted as a string lying along a potential, the washboard potential (WP) U(ϕ, x, t), given by…”

“…Equation (7) is numerically solved within the Ito scheme by setting ∆t = ∆x = 0.05. The MST τ is a nonlinear relaxation time (NLRT) [14,17,81,91] and represents the mean value of the permanence times of the phase ϕ within the first valley,…”

“…The dynamics of these devices is affected by environmental perturbations and, in particular, by random fluctuations responsible for decoherence phenomena. The effects of both thermal and non-thermal random fluctuations on the behavior of normal and graphene-based JJs were recently investigated [17,[79][80][81].…”