Induced quantum numbers of a magnetic vortex at nonzero temperature

TL;DR

This paper investigates how topological defects like magnetic vortices induce various quantum numbers in a fermionic system at finite temperature, revealing their dependence on temperature, flux, and boundary conditions.

Contribution

It provides a comprehensive analysis of thermal averages and correlations of induced quantum numbers in a relativistic electron gas with magnetic vortices, including resolving the angular momentum definition issue.

Findings

Induced quantum numbers depend on temperature, flux, and boundary conditions.

Thermal fluctuations restrict the boundary parameter range.

The angular momentum definition for the system is clarified.

Abstract

The phenomenon of the finite-temperature induced quantum numbers in fermionic systems with topological defects is analyzed. We consider an ideal gas of twodimensional relativistic massive electrons in the background of a defect in the form of a pointlike magnetic vortex with arbitrary flux. This system is found to acquire, in addition to fermion number, also orbital angular momentum, spin, and induced magnetic flux, and we determine the functional dependence of the appropriate thermal averages and correlations on the temperature, the vortex flux, and the continuous parameter of the boundary condition at the location of the defect. We find that nonnegativeness of thermal quadratic fluctuations imposes a restriction on the admissible range of values of the boundary parameter. The long-standing problem of the adequate definition of total angular momentum for the system considered is resolved.