Phase behavior and collective excitations of the Morse ring chain

Using primarily numerical methods we study clustering processes and collective excitations in a one-dimensional ring chain. The ring chain is constituted by N identical point particles with next neighbors interacting via nonlinear Morse springs. If the system is coupled to a heat bath (Gaussian white noise and viscous friction), then depending on the particle density and the bath temperature different phase-like states can be distinguished. This will be illustrated by means of numerically calculated phase diagrams. In order to identify collective excitations activated by the heat bath we calculate the spectrum of the normalized dynamical structure factor (SDF). Our numerical results show that the transition regions between different phase-like states are typically characterized by a 1/f-type SDF spectrum, reflecting the fact that near critical points correlations on all length and time scales become important. In the last part of the paper we also discuss a non-equilibrium effect, which occurs if an additional nonlinearly velocity-dependent force is included in the equations of motions. In particular it will be shown that such additional dissipative effects may stabilize cluster configurations. Copyright Springer-Verlag Berlin/Heidelberg 2003