Vacuum energy induced by an impenetrable flux tube of finite radius

TL;DR

This paper investigates how a finite-radius magnetic flux tube influences the vacuum energy of a charged scalar field, revealing periodic dependence on flux and analyzing spatial and curvature effects.

Contribution

It extends previous work by examining smaller flux tube radii and larger distances, providing a comprehensive analysis of vacuum energy dependence.

Findings

Vacuum energy is periodic in the magnetic flux enclosed.

Vacuum energy density depends on distance from the flux tube.

Coupling to space-time curvature affects vacuum energy distribution.

Abstract

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. Our previous study in J. Phys. A: Vol.43, 175401 (2010) is extended to the case of smaller radius of the tube and larger distances from it. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.