Quantum Mechanics and Thermodynamics of Particles with Distance Dependent Statistics

TL;DR

This paper explores how distance-dependent statistics affect quantum particles, deriving formulas for their thermodynamic behavior and connecting to known anyon results in specific limits.

Contribution

It introduces a framework for distance-dependent statistics in anyon-like systems and derives a general formula for the second virial coefficient.

Findings

Derived a general formula for the second virial coefficient.

Reproduces known results for ideal anyons in limiting cases.

Analyzed the two-body problem for particles with distance-dependent statistics.

Abstract

The general notion of distance dependent statistics in anyon-like systems is discussed. The two-body problem for such statistics is considered, the general formula for the second virial coefficient is derived and it is shown that in the limiting cases it reproduces the known results for ideal anyons.