Slowest kinetic modes revealed by metabasin renormalization

TL;DR

This paper introduces a new method combining metabasin analysis and Jacobi iteration to efficiently identify the slowest relaxation modes in high-dimensional kinetic systems, demonstrated on models and ionic nanoparticle vacancy transport.

Contribution

It presents a novel approach for extracting long-time relaxation dynamics by renormalizing kinetic equations, enabling analysis of complex systems without full diagonalization.

Findings

Successfully applied to a four-funnel model for slow mode identification.

Enabled physical interpretation of relaxation as two successive processes.

Validated on vacancy transport in ionic nanoparticles.

Abstract

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009)] and a Jacobi method. We test the method on a illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al. Chem. Phys. Lett. 654, 52 (2016)], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.