English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The possibility that like-charges can attract each other under the mediationof mobile counterions is by now well documented experimentally, numerically,and analytically. Yet, obtaining exact results is in general impossible, orrestricted to some limiting cases. We work out here in detail a one dimensionalmodel that retains the essence of the phenomena present in higher dimensionalsystems. The partition function is obtained explicitly, from which a wealth ofrelevant quantities follow, such as the effective force between the charges orthe counterion profile in their vicinity. Isobaric and canonical ensembles aredistinguished. The case of two equal charges screened by an arbitrary number$N$ of counterions is first studied, before the more general asymmetricsituation is addressed. It is shown that the parity of $N$ plays a key role inthe long range physics.

Screening like-charges in one-dimensional Coulomb systems: Exact results