Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability

Abstract

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influence of the mode's starting frequency on the results and their robustness against an additional thermal background are also addressed.

ac-locking of thermally-induced sine-Gordon breathers

“…Both panels demonstrate that, in the presence of thermal fluctutations and ac forcing, remarkably stable breather excitations can form in the junction. In a purely dissipative case, breathers radiatively decay within ∼ 1/α = 5 [23], a lifetime which is surpassed by multiple orders of magnitude here. Note also the stability of the modes with respect to the position, i.e., their centers do not drift away from the originary positions [x ≈ −16.5 in Fig.…”

“…Due to its nontopological structure, mastering the breather's physics is a very tough challenge. In particular, experimental evidence of this oscillating state has yet to be provided in LJJs, despite the numerous investigations on the matter [17][18][19][20][21][22][23], primarily due to its friction-triggered radiative decay and its elusiveness with respect to I -V measurements [20,24]. The Josephson breather's detection would, therefore, solve a long-lasting problem in nonlinear science, but it would also pave the way for several applications in, e.g., information transmission [25], quantum computation [26], generation of THz radiation [27].…”