Persistent Current of Free Electrons in the Plane

TL;DR

This paper revises predictions about persistent currents of free electrons in the plane by applying zeta function regularization, revealing a linear flux dependence and antisymmetry, with discussions on self-adjoint extensions and resonances.

Contribution

It introduces a zeta function regularization approach that alters the predicted behavior of persistent currents, highlighting the importance of self-adjoint extensions and resonances.

Findings

Persistent current varies linearly with flux.

Current is antisymmetric with respect to all time-preserving flux values.

Regularization changes the qualitative behavior of the current.

Abstract

Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $\alpha$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.