Second Virial Coefficient for Noncommutative Space

TL;DR

This paper derives the second virial coefficient for particles in a noncommutative 2D space under a magnetic field, linking it to anyon statistics and composite fermions, especially in high-temperature limits.

Contribution

It introduces a novel interpretation of the second virial coefficient in noncommutative space, connecting it to anyon statistics and composite fermions.

Findings

Relation between noncommutativity parameter and anyon statistics in high-temperature limit

Expression of the virial coefficient in terms of composite fermions

Interpretation of noncommutative effects as anyonic behavior

Abstract

The second virial coefficient $B_{2}^{nc}(T)$ for non-interacting particles moving in a two-dimensional noncommutative space and in the presence of a uniform magnetic field $\vec B$ is presented. The noncommutativity parameter $\te$ can be chosen such that the $B_{2}^{nc}(T)$ can be interpreted as the second virial coefficient for anyons of statistics $\al$ in the presence of $\vec B$ and living on the commuting plane. In particular in the high temperature limit $\be\lga 0$, we establish a relation between the parameter $\te$ and the statistics $\al$. Moreover, $B_{2}^{nc}(T)$ can also be interpreted in terms of composite fermions.