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Velizhanin KA, Piryatinski A, Chernyak VY. Low-temperature hopping dynamics with energy disorder: renormalization group approach. J Chem Phys. 2013;139(8):084118doi: 10.1063/1.4819197.
Velizhanin, K. A., Piryatinski, A., & Chernyak, V. Y. (2013). Low-temperature hopping dynamics with energy disorder: renormalization group approach. The Journal of chemical physics, 139(8), 084118. https://doi.org/10.1063/1.4819197
Velizhanin, Kirill A, et al. "Low-temperature hopping dynamics with energy disorder: renormalization group approach." The Journal of chemical physics vol. 139,8 (2013): 084118. doi: https://doi.org/10.1063/1.4819197
Velizhanin KA, Piryatinski A, Chernyak VY. Low-temperature hopping dynamics with energy disorder: renormalization group approach. J Chem Phys. 2013 Aug 28;139(8):084118. doi: 10.1063/1.4819197. PMID: 24006985.
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J Chem Phys. 2013 Aug 28;139(8):084118. doi: 10.1063/1.4819197.

Low-temperature hopping dynamics with energy disorder: renormalization group approach.

The Journal of chemical physics

Kirill A Velizhanin, Andrei Piryatinski, Vladimir Y Chernyak

Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

PMID: 24006985 DOI: 10.1063/1.4819197

Abstract

We formulate a real-space renormalization group (RG) approach for efficient numerical analysis of the low-temperature hopping dynamics in energy-disordered lattices. The approach explicitly relies on the time-scale separation of the trapping/escape dynamics. This time-scale separation allows to treat the hopping dynamics as a hierarchical process, RG step being a transformation between the levels of the hierarchy. We apply the proposed RG approach to analyze hopping dynamics in one- and two-dimensional lattices with varying degrees of energy disorder, and find the approach to be accurate at low temperatures and computationally much faster than the brute-force direct diagonalization. Applicability criteria of the proposed approach with respect to the time-scale separation and the maximum number of hierarchy levels are formulated. RG flows of energy distribution and pre-exponential factors of the Miller-Abrahams model are analyzed.

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