ALGEBRAIC RELAXATION LAWS FOR CLASSICAL PARTICLES IN 1D ANHARMONIC POTENTIALS

Using extensive numerical analysis and exact calculations we show that the relaxation of a classical particle in 1D anharmonic potential lan dscapes with a leading quartic term follows a lit decay law at all tem peratures, leading to a logarithmically increasing mean square displac ement. For leading anharmonic terms of forth x(2n) we find that the as ymptotic relaxation is consistent with 1/t(phi), where phi = 1/(n - 1) at all temperatures. We briefly comment on the possible implications of this result in the study of displacive structural transitions and i n complex systems.