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Collision bias and vacancy selection in rare-current fluctuations

Year: 2026
Type: preprint
Abstract: Vacancies remove charge carriers, but they also remove collisions that limit charge transfer. We study this competition in a charged lattice gas with unequal ordered exchange probabilities and ballistic vacancies. After exact vacancy deletion, the two incoming occupation counts become the side lengths of a six-vertex network. Small depletion lowers the polarized-network capacity; carrying a current above the dense capacity without collective atypical scattering therefore requires a finite beam imbalance. At fixed vacancy density, vacancies extend the current sector with probability cost linear in time precisely when the dense capacity lies below the collision-free single-beam value. In this regime, the long-time limit with subexponentially vanishing vacancy density selects two explicit asymmetric occupation profiles. Their vacancy fraction remains positive as the current threshold then approaches the dense capacity from above, whereas it vanishes at or below that capacity. Exponential dilution places initial preparation and scattering on the same quadratic probability scale. A local rate expansion uniform for aspect ratios near one, together with the exclusion of intermediate occupations, establishes a first-order switch between the globally minimizing sectors near onset. Independent variational calculations resolve finite-excess corrections, while exhaustive finite-time calculations with stationary random charge colors show a crossover toward asymmetric incoming occupations. The record contains the preprint and a reproducibility archive with the LaTeX source, figures, numerical data, C++ and Python code, independent benchmarks, and instructions for regenerating the results.
DOI: 10.5281/zenodo.24090796
Author: Jiang, Weiqi
Language: English
Open Access status: green
OpenAlex ID: W7225644804
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