Casimir effect for scalar current densities in topologically nontrivial spaces

Abstract

We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation.

25 pages, 5 figures, PACS numbers: 03.70.+k, 11.10.Kk, 04.20.Gz

References in corpus (26)

• The electronic properties of graphene
• Flux Compactification
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Chiral Gauge Theory for Graphene
• Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Kaluza-Klein models as pistons
• Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
• Quantum field theory on toroidal topology: algebraic structure and applications
• The Casimir force on a piston in the spacetime with extra compactified dimensions
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Comment on: "The Casimir force on a piston in the spacetime with extra compactified dimensions" [Phys. Lett. B 668 (2008) 72]
• The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions
• Improved constraints on the coupling constants of axion-like particles to nucleons from recent Casimir-less experiment
• Induced vacuum currents in anti-de Sitter space with toral dimensions
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Vortex and gap generation in gauge models of graphene
• Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Dark energy and the hierarchy problem
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Electromagnetic Casimir piston in higher dimensional spacetimes

Cited by in corpus (11)

• Vacuum currents in braneworlds on AdS bulk with compact dimensions
• Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-branes geometry
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Fermionic currents in AdS spacetime with compact dimensions
• Fermionic currents in topologically nontrivial braneworlds
• Induced fermionic charge and current densities in two-dimensional rings
• Vacuum polarization near boundaries
• Vacuum currents in curved tubes
• Fermionic vacuum stresses in models with toroidal compact dimensions
• Vacuum currents in elliptic pseudosphere tubes
• Topological Casimir effect in models with helical compact dimensions