Casimir effect in hemisphere capped tubes

Abstract

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2+1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.

24 pages, 5 figures

References in corpus (18)

• The electronic properties of graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Chiral Gauge Theory for Graphene
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime
• Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Finite temperature fermionic condensate and currents in topologically nontrivial spaces
• Polarization of the fermionic vacuum by a global monopole with finite core
• Vortex and gap generation in gauge models of graphene
• Chiral Symmetry Restoration in Anisotropic QED(3)
• Scalar Casimir Effect on a D-dimensional Einstein Static Universe
• Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime
• Casimir densities from coexisting vacua
• Vacuum polarization by a global monopole with finite core
• Zeta Determinant for Laplace Operators on Riemann Caps
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Vacuum densities for a thick brane in AdS spacetime

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