Abstract
We perform numerical simulations of the dynamical behavior of a sine-Gordon chain in a heat bath. The interaction with the heat bath is simulated by the Langevin formalism. The noise term in uncorrelated in both space and time. We use the Karhunen-Loeve decomposition to study the effective number of degrees of freedom as a function of temperature (i.e., of the noise dispersion). At low temperatures we find a spatially disordered regime, characterized by a high number of degrees of freedom. At a temperature of the order of the soliton rest mass we find a relatively sharp crossover to an ordered regime, characterized by a low number of degrees of freedom. The spatial structure of the modes suggests that the transition is associated to the appearance of thermally activated solitons. We also present an alternative estimate of the effective number of degrees of freedom.
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