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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Anyon systems are studied in connection with several interesting applicationsincluding high $T_C$ superconductivity and topological quantum computing. Inthis work we show that these systems can be realized starting from directedpolymers braided together to form a nontrivial link configuration belonging tothe topological class of plats. The statistical sum of a such plat is relatedhere to the partition function of a two-component anyon gas. The constraintsthat preserve the topological configuration of the plat are imposed on thepolymer trajectories using the so-called Gauss linking number, a topologicalinvariant that has already been well studied in polymer physics. Due to theseconstraints, short-range forces act on the monomers or, equivalently, on theanyon quasiparticles in a way that closely resembles the appearance of reactionforces in the constrained systems of classical mechanics. If the polymers arehomogeneous, the anyon system reaches a self-dual point, in which these forcesvanish exactly. A class of self-dual solutions that minimize the energy of theanyons is derived. The two anyon gas discussed here obeys an abelianstatistics, while for quantum computing it is known that nonabelian anyons arenecessary. However, this is a limitation due to the use of the Gauss linkinginvariant to impose the topological constraints, which is a poor topologicalinvariant and is thus unable to capture the nonabelian characteristics of thebraided polymer chains. A more refined treatment of the topological constraintswould require more sophisticated topological invariants, but so far theirapplication to the statistical mechanics of linked polymers is an open problem.

Polymer plats and multicomponent anyon gases