Mean first passage times reconstruct the slowest relaxations in potential energy landscapes of nanoclusters

TL;DR

This paper demonstrates how the slowest relaxation rates in nanoclusters can be reconstructed from mean first passage times, revealing the influence of heterogeneity in potential energy landscapes and using a novel stationary population method.

Contribution

It introduces a method to reconstruct slow relaxation times from first passage times and explains their origin in heterogeneous energy landscapes of nanoclusters.

Findings

Relaxation modes are linked to first passage times.

Heterogeneity in activation energies causes different diffusivities.

The stationary population method enables symmetric computation of first passage times.

Abstract

Relaxation modes are the collective modes in which all probability deviations from equilibrium states decay with the same relaxation rates. In contrast, a first passage time is the required time for arriving for the first time from one state to another. In this paper, we discuss how and why the slowest relaxation rates of relaxation modes are reconstructed from the first passage times. As an illustrative model, we use a continuous-time Markov state model of vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all characteristics of the relaxations in KCl nanoclusters come from the fact that they are hybrids of two kinetically different regions of the fast surface and slow bulk diffusions. The origin of the different diffusivities turns out to come from the heterogeneity of the activation energies on the potential energy landscapes. We also develop a stationary population method to compute the mean first passage times as mean times required for pair annihilations of particle-hole pairs, which enables us to obtain the symmetric results of relaxation rates under the exchange of the sinks and the sources. With this symmetric method, we finally show why the slowest relaxation times can be reconstructed from the mean first passage times.