Zero-point energy of N perfectly conducting concentric cylindrical shells

We evaluate the positive-frequency Wightman function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling for a cylindrical shell in background of dS spacetime. The field is prepared in the Bunch-Davies vacuum state and on the shell the corresponding operator obeys Robin boundary condition. In the region inside the shell and for non-Neumann boundary conditions, the Bunch-Davies vacuum is a physically realizable state for all values of the mass and curvature coupling parameter. For both interior and exterior regions, the VEVs are decomposed into boundary-free dS and shell-induced parts. We show that the shell-induced part of the vacuum energy-momentum tensor has a nonzero off-diagonal component corresponding to the energy flux along the radial direction. Unlike to the case of a shell in Minkowski bulk, for dS background the axial stresses are not equal to the energy density. In dependence of the mass and of the coefficient in the boundary condition, the vacuum energy density and the energy flux can be either positive or negative. The influence of the background gravitational field on the boundary-induced effects is crucial at distances from the shell larger than the dS curvature scale. In particular, the decay of the VEVs with the distance is power-law (monotonic or oscillatory with dependence of the mass) for both massless and massive fields. For Neumann boundary condition the decay is faster than that for non-Neumann conditions.

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“…where 22) and F (a, b; c; w) is the hypergeometric function. The function (2.21) is the Wightman function for the boundary-free dS spacetime.…”

Section: Interior Regionmentioning

confidence: 99%

“…For a cylindrical shell in the Minkowski bulk and for a massive field the VEV of the field squared decays exponentially with the distance from the shell. For purely imaginary values of the parameter ν and for A = 0 the leading asymptotic term is in the form 22) where the constants M (e) and φ (e) are defined by the relation…”

Section: Exterior Regionmentioning

confidence: 99%

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Saharian

Manukyan

2014

Class. Quantum Grav.

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“…1) and we shall not include improvements possible via the proximity force theorem. [203][204][205] Although such refinements can be implemented by means of well-known prescriptions, at the price of further complicating the numerical implementation of the Lifshitz theory (see Sec. C below), our emphasis at this stage is on highlighting as transparently as possible the physical foundations of a dispersion force accelerator.…”

Section: B Lifshitz Theorymentioning

confidence: 99%

Nanopropulsion from High-Energy Particle Beams via Dispersion Forces in Nanotubes

Pinto¹

2012

48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Amp;amp; Exhibit

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Here we show for the first time that the van der Waals forces which act on the inner cores of multiwalled nanotubes can be altered to produce high-energy, high-luminosity neutral beams of nano-shuttles sliding inside the outer shells until they are ejected. This novel principle of nanotube core acceleration is based on a nanoscale implementation of dispersion force manipulation originally introduced and then developed both theoretically and experimentally by the author in micro-electromechanical systems (MEMS). In analogy with electromagnetic neutral particle acceleration, the van der Waals force, which has been experimentally observed to "retract" partially extruded cores inside the outer nanotube shells at extremely high speeds, is modulated in order to transfer a net amount of kinetic energy to the accelerated beam. Since dispersion forces are a dominant interaction at typical interlayer distances ≈ 0.34 nm, and sliding frictional forces are relatively small, the resulting final speed of the ejected shells can exceed vcore,fin 10 km/s. Technologies for the synthesis, fabrication, and uncapping of dense arrays of parallel, telescoping, multiwalled nanotubes have been already demonstrated to yield surface densities 10 10 cm −2 and individual nanotube lengths 10 cm have been demonstrated. Therefore, as the technology becomes fully developed, the resulting net thrust and specific impulse of a nanopropulsion device based on this approach can be shown to decisively exceed that of other existing lowthrust technologies. Additional advantages include the neutrality of ejecta, the potential for a tight integration of the propulsive system with on-chip digital management, and system versatility to accommodate drastically different mission profiles.

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“…Moreover, the exact result for the Casimir interactions between a finite number of compact objects of arbitrary shape and separation have been developed by using the functional determinant or multiple scattering approach [16,17,18,19,20,21]. Besides, the Casimir force problems of two concentric spheres [22,23,24,25,26] and two concentric cylinders [27,28,29] have also been calculated by using different regularization method recently.…”

Section: Introductionmentioning

confidence: 99%

Scalar Casimir effect between two concentric spheres

Ozcan

2012

Preprint

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The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We devoleped a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, (η = a−b √ ab where a (b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

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Zero-point energy of N perfectly conducting concentric cylindrical shells

Cited by 10 publications

References 36 publications

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Nanopropulsion from High-Energy Particle Beams via Dispersion Forces in Nanotubes

Scalar Casimir effect between two concentric spheres

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