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Collective transport in the discrete Frenkel-Kontorova model

2013/05/31 by Thomas D. Swinburne, T. D. Swinburne · 8 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chain (unit) #Fokker–Planck equation #Harmonic #Mathematical analysis #Mathematics #Nonlinear system #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Thermal diffusivity #Upper and lower bounds #cond-mat.mes-hall #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physreve.88.012135

published in Physical Review E 88(1), 012135 (American Physical Society) · 7 pages, 3 figures, submitted

arxiv created 2013/07/15 · openalex publication_date 2013/07/29 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model. Significantly, it is shown that the free energy barrier is a lower bound to the true finite temperature migration barrier for this general and popular system. Numerical simulation confirms the analysis, while effective migration potentials implied by the bounds are employed to give a surprisingly accurate prediction of the nonlinear response.

Citations