ASYMPTOTIC DEPENDENCE OF THE RESIDUAL ENERGY ON ANNEALING TIME

In order to find a low-energy state through annealing, one generally must immerse a system in a heat bath for a long time. Asymptotic dependence of the resultant energy epsilon on time tau spent in annealing is a matter of current interest. By comparing the established scaling forms of epsilon(tau) for three kinds of systems, we propose that the functional form of 'density of local minima' D(E) is a key to the determination of scaling epsilon(tau). For instance, epsilon is-proportional-to 1/ln tau if D(E) is-proportional-to E-alpha. Numerical simulation of one-dimensional white-noise potential models is carried out to examine the conjecture. The result is consistent with the conjecture.