STOCHASTICALLY-DRIVEN COHERENCE IN A SINE-GORDON CHAIN

We perform numerical simulations of the dynamical behavior of a sine-G ordon chain in a heat bath. The interaction with the heat bath is simu lated by the Langevin formalism. The noise term is uncorrelated in bot h 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 spatiall y disordered regime, characterized by a high number of degrees of free dom. At a temperature of the order of the soliton rest mass we find a relatively sharp crossover to an ordered regime, characterized by a lo w number of degrees of freedom. The spatial structure of the modes sug gests that the transition is associated to the appearance of thermally activated solitons. We also present an alternative estimate of the ef fective number of degrees of