Noisy sine-Gordon breather dynamics: A short review

Abstract

The aim of this review is to address recent developments in the emergence and dynamics of sine-Gordon (SG) breathers under dissipation, external drives, and environmental noise. We then discuss various strategies for breather detection in a specific physical platform: the long Josephson junction (LJJ). We note that our findings rely on a rather general SG framework, whose importance extends well beyond the scope of Josephson electronics. While the results hold significance in contexts involving nonequilibrium and collective phenomena, we also emphasize their connection to the Josephson world, as they provide direct insights relevant to that domain. To set the stage for our discussions in the Josephson context, we begin by deriving the celebrated Josephson relations. From the basic Josephson junction building block, we obtain the SG model for the electrodynamics of the LJJ and provide an overview of the model's properties. We then discuss recent research findings on: (i) supratransmission-induced traveling breathers and their detection; (ii) the noise-enhanced stability effect on breather dynamics; (iii) the AC-locking of noise-induced breathers and their statistical (resistive switching) signature; (iv) the thermal transport fingerprint of Josephson breathers.