Vacuum currents in curved tubes

Abstract

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on rotationally symmetric 2D curved tubes. For a general spatial geometry and for quasiperiodicity condition with a general phase, the representation of the Hadamard function is provided where the topological contribution is explicitly extracted. As an important local characteristic of the vacuum state the expectation value of the current density is studied. The vacuum current is a periodic function of the magnetic flux enclosed by the tube with the period of flux quantum. The general formula is specified for constant radius and conical tubes. As another application, we consider the Hadamard function and the vacuum current density for a scalar field on the Beltrami pseudosphere. Several representations are provided for the corresponding expectation value. For small values of the proper radius of the tube, compared with the curvature radius, the effect of spatial curvature on the vacuum current is weak and the leading term in the corresponding expansion coincides with the current density on a constant radius tube. The effect of curvature is essential for proper radii of the tube larger than the radius of spatial curvature. In this limit the fall-off of the current density, as a function of the proper radius, follows a power-law for both massless and massive fields. This behavior is in clear contrast to the one for a constant radius tube with exponential decay for massive fields. We also compare the vacuum currents on the Beltrami pseudosphere and on locally de Sitter and anti-de Sitter 2D tubes.

27 pages, 5 figures, details of qauntization procedure and discussion added

References in corpus (15)

• The electronic properties of graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Persistent currents in normal metal rings
• Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
• Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
• Pseudo-magnetic field in curved graphene
• Vacuum currents induced by a magnetic flux around a cosmic string with finite core
• Gauge fields and curvature in graphene
• Induced vacuum bosonic current by magnetic flux in a higher dimensional compactified cosmic string spacetime
• Induced vacuum currents in anti-de Sitter space with toral dimensions
• Negative-curvature spacetime solutions for graphene
• Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces
• Graphene, Dirac equation and analogue gravity
• Induced fermionic charge and current densities in two-dimensional rings

Cited by in corpus (5)

• SUSY design of smooth quantum rings in graphene
• Finite temperature fermionic charge and current densities in conical space with a circular edge
• Vacuum currents in elliptic pseudosphere tubes
• Scalar vacuum densities on Beltrami pseudosphere
• Fermionic Casimir densities for a uniformly accelerating mirror in the Fulling-Rindler vacuum