Screening like-charges in one-dimensional Coulomb systems: Exact results
Abstract
The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted to some limiting cases. We work out here in detail a one dimensional model that retains the essence of the phenomena present in higher dimensional systems. The partition function is obtained explicitly, from which a wealth of relevant quantities follow, such as the effective force between the charges or the counterion profile in their vicinity. Isobaric and canonical ensembles are distinguished. The case of two equal charges screened by an arbitrary number of counterions is first studied, before the more general asymmetric situation is addressed. It is shown that the parity of plays a key role in the long range physics.
Keywords
Cite
@article{arxiv.1507.06281,
title = {Screening like-charges in one-dimensional Coulomb systems: Exact results},
author = {Gabriel Tellez and Emmanuel Trizac},
journal= {arXiv preprint arXiv:1507.06281},
year = {2016}
}