Fractionalization of angular momentum at finite temperature around a magnetic vortex

TL;DR

This paper resolves the ambiguity in defining angular momentum for a quantum particle around a magnetic vortex at finite temperature by using second-quantization, providing clear thermal averages and fluctuations for a relativistic Fermi gas.

Contribution

It introduces a definitive kinetic-based definition of angular momentum in a finite-temperature quantum vortex system, clarifying longstanding ambiguities.

Findings

Unambiguous kinetic definition of angular momentum established

Calculated thermal averages and fluctuations for the Fermi gas

Demonstrated plausible behavior of angular momentum fluctuations

Abstract

Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.