Induced vacuum current and magnetic flux in quantum scalar matter in the background of a vortex defect with the Neumann boundary condition

Abstract

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

arXiv comment12 pages, 2 figures

References in corpus (17)

• Cosmic strings
• The Ginzburg-Landau Theory of Type II superconductors in magnetic field
• Topological Defects and Structure Formation
• Cosmic Strings and Superstrings
• An Introduction to Spontaneous Symmetry Breaking
• Gamma ray bursts from superconducting cosmic strings
• The Casimir-Aharonov-Bohm effect?
• Gravitational Radiation by Cosmic Strings in a Junction
• Gravitational Wave Bursts from Cosmic Superstring Reconnections
• One-Loop Effective Action for the Extended Spinor Electrodynamics with Violation of Lorentz and CPT Symmetry
• Polarization of the vacuum of a quantized scalar field by an impenetrable magnetic vortex of finite thickness
• Vacuum energy induced by an impenetrable flux tube of finite radius
• Induced vacuum magnetic flux in quantum spinor matter in the background of a topological defect in two-dimensional space
• Properties of the ground state of electronic excitations in carbon-like nanocones
• Casimir energy and force induced by an impenetrable flux tube of finite radius
• Induced vacuum current and magnetic field in the background of a vortex
• Induced vacuum magnetic field in the cosmic string background

Cited by in corpus (4)

• Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background
• Induced vacuum energy density of quantum charged scalar matter in the background of an impenetrable magnetic tube with the Neumann boundary condition
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
• Magnetic field in vacuum of quantum spinor matter induced by a cosmic string in three-dimensional space