Velocity statistics for interacting edge dislocations in one dimension from Dyson’s Coulomb gas model

摘要

The dynamics of edge dislocations with parallel Burgers vectors, moving in the same slip plane, is mappednonto Dyson’s model of a two-dimensional Coulomb gas confined in one dimension. We show that the tailndistribution of the velocity of dislocations is power law in form, as a consequence of the pair interaction ofnnearest neighbors in one dimension. In two dimensions, we show the presence of a pairing phase transition in ansystem of interacting dislocations with parallel Burgers vectors. The scaling exponent of the velocity distributionnat effective temperatures well below this pairing transition temperature can be derived from the nearest-neighborninteraction, while near the transition temperature, the distribution deviates from the form predicted by thennearest-neighbor interaction, suggesting the presence of collective effects.