Two-step relaxation mode analysis with multiple evolution times: Application to a single [n]polycatenane

A method of two-step relaxation mode analysis (RMA) with multiple evolution times is proposed. In this method, the usual RMA with a single evolution time is first applied to relevant physical quantities. Then, RMA is again applied to a portion of the slowest relaxation modes obtained by the first RMA, where the evolution time for each mode is determined from its relaxation rate. The first step gives a rough estimate of the relaxation modes and rates, while the second step reduces the degrees of freedom and refines the estimate. The effectiveness of the method was demonstrated by its application to a Brownian dynamics simulation of a single [n]polycatenane in the free-draining limit.