Induced Vacuum Energy Density of Quantum Charged Scalar Matter in the Background of an Impenetrable Magnetic Tube with the Neumann Boundary Condition

We consider the vacuum polarization of a charged scalar matter field outside tube with magnetic flux inside. The is impenetrable for quantum matter, and perfectly rigid (Neumann) boundary condition imposed at its surface. write expressions induced energy density case space arbitrary dimension an value flux. do numerical computation half-integer in London units (2 + 1)-dimensional space-time. show that induced, if Compton wavelength exceeds transverse size considerably. periodic tube, providing quantumfield-theoretical manifestation Aharonov–Bohm effect. dependencies upon distance from center different values thickness are obtained. results compared to those obtained earlier reflecting (Dirichlet) condition. It shown Neumann greater than Dirichlet