Stochastic 'fuzzy confinement' of intrinsic localised modes

Abstract

The long time diffusive behaviour of intrinsic localised modes (discrete breathers) in the discrete damped-driven sine-Gordon chain under Gaussian white noise (to simulate temperature) is studied. We present a theoretical model for an approximate description of the diffusion, derive an expression for the diffusion constant and compare with results from simulations. It turns out that an increase of the temperature inhibits the diffusive motion in such a way that the breather, propagating with a well-defined velocity in the noise-free case, is almost pinned. As all physical processes in the real world occur at temperatures T > 0, these results also have a bearing on the experimental detection of mobile breathers, e.g. in parallel arrays of Josephson junctions.