Induced Vacuum Current and Magnetic Flux in Quantum Scalar Matter in the Background of a Vortex Defect with the Neumann Boundary Condition

A topological defect in the form of Abrikosov-Nielsen-Olesen vortex a space arbitrary dimension is considered as gauge-flux-carrying tube that impenetrable for quantum matter. Charged scalar matter field quantized background with perfectly rigid (Neumann) boundary condition imposed at side surface vortex. We show current circulating around induced vacuum, if Compton wavelength exceeds transverse size considerably. The vacuum periodic value gauge flux vortex, providing quantum-field-theoretical manifestation Aharonov-Bohm effect. leads to appearance an magnetic some values thickness by singular filament. results were compared obtained earlier case reflecting (Dirichlet) It shown absolute and Neumann greater than Dirichlet condition.