Noise-Induced Organization in a Sine-Gordon Chain

The appearance of thermally activated solitons in a sine-Gordon system is related to the roughening exponent 5, defined as the scaling exponent of the length of the ensemble average of the standard deviation of tire height of the spatiotemporal profile. Before the onset of the noi~-educed ~sition to the solito~c regime, the roug~n~g exponent is zero as it is for a white noise signal. After the activation of solitons, there is a very interesting crossover from non-KPZ behavior (c- 0.70) to KPZ behavior (c- 0.50); additionally, for sufficiently large scales, a crossover to a zero roughening exponent takes place. In this paper we precise the underlying dynamics of the different regimes that appear at different scales via geometric chignon as the size of the system and the friction c~f~cient are varied.