Slowest kinetic modes revealed by metabasin renormalization

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.

arXiv comment5 pages, 3 figures

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Cited by in corpus (3)

• Manipulating the Glass Transition in Nanoscale
• Changes of graph structure of transition probability matrices indicate the slowest kinetic relaxations
• Mean first passage times reconstruct the slowest relaxations in potential energy landscapes of nanoclusters