arXiv subjects

A. A. Saharian

Publications and source records attributed to A. A. Saharian.

At least 127 records · Page 7Linked to original sources

arXiv2010

Casimir effect for parallel plates in de Sitter spacetime

The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows to explicitly extract the contributions to the expectation values which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power-law (monotonic or oscillating), with independence of the value of the field mass.

hep-th↗

arXiv2009

Casimir densities for a boundary in Robertson-Walker spacetime

For scalar and electromagnetic fields we evaluate the vacuum expectation value of the energy-momentum tensor induced by a curved boundary in the Robertson--Walker spacetime with negative spatial curvature. In order to generate the vacuum densities we use the conformal relation between the Robertson-Walker and Rindler spacetimes and the corresponding results for a plate moving by uniform proper acceleration through the Fulling--Rindler vacuum. For the general case of the scale factor the vacuum energy-momentum tensor is presented as the sum of the boundary free and boundary induced parts.

hep-th↗

arXiv2009

Topological Casimir effect in power-law FRW cosmologies

We investigate the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. When the comoving lengths of the compact dimensions are short compared to the Hubble length, the topological parts coincide with those for a conformal coupling. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values.

hep-th↗

arXiv2009

Topological Casimir effect in nanotubes and nanoloopes

The Casimir effect is investigated in cylindrical and toroidal carbon nanotubes within the framework of the Dirac-like model for the electronic states. The topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications. For finite length metallic nanotubes the Casimir forces acting on the tube edges are always attractive, whereas for semiconducting-type ones they are attractive for small lengths of the nanotube and repulsive for large lengths.

hep-th↗

arXiv2009

Casimir densities for a plate in de Sitter spacetime

Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with general curvature coupling parameter in the geometry of a plate in the de Sitter spacetime. Robin boundary condition for the field operator is assumed on the plate. The vacuum expectation values are presented as the sum of two terms. The first one corresponds to the geometry of de Sitter bulk without boundaries and the second one is induced by the presence of the plate. We show that for non-conformal fields the vacuum energy-momentum tensor is non-diagonal with the off-diagonal component corresponding to the energy flux along the direction perpendicular to the plate. In dependence of the parameters, this flux can be either positive or negative. The asymptotic behavior of the field squared, vacuum energy density and stresses near the plate and at large distances is investigated.

hep-th↗

arXiv2009

Vacuum fluctuations and topological Casimir effect in Friedmann-Robertson-Walker cosmologies with compact dimensions

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological parts coincide with those for a conformal coupling and they are related to the corresponding quantities in the flat spacetime by standard conformal transformation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values. In the monotonic regime and for nonconformally and nonminimally coupled fields the vacuum stresses are isotropic and the equation of state for the topological parts in the energy density and pressures is of barotropic type. In the oscillatory regime, the amplitude of the oscillations for the topological part in the expectation value of the field squared can be either decreasing or increasing with time, whereas for the energy-momentum tensor the oscillations are damping.

hep-th↗

arXiv2009

Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes

We evaluate the Casimir energy and force for a massive fermionic field in the geometry of two parallel plates on background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions. The bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The Casimir energy is decomposed into purely topological, single plate and interaction parts. With independence of the lengths of the compact dimensions and the phases in the periodicity conditions, the interaction part of the Casimir energy is always negative. In order to obtain the resulting force, the contributions from both sides of the plates must be taken into account. Then, the forces coming from the topological parts of the vacuum energy cancel out and only the interaction term contributes to the Casimir force. Applications of the general formulae to Kaluza-Klein type models and carbon nanotubes are given. In particular, we show that for finite length metallic nanotubes the Casimir forces acting on the tube edges are always attractive, whereas for semiconducting-type ones they are attractive for small lengths of the nanotube and repulsive for large lengths.

hep-th↗

arXiv2009

Casimir energy and the possibility of higher dimensional manipulation

It is well known that the Casimir effect is an excellent candidate for the stabilization of the extra dimensions. It has also been suggested that the Casimir effect in higher dimensions may be the underlying phenomenon that is responsible for the dark energy which is currently driving the accelerated expansion of the universe. In this paper we suggest that, in principle, it may be possible to directly manipulate the size of an extra dimension locally using Standard Model fields in the next generation of particle accelerators. This adjustment of the size of the higher dimension could serve as a technological mechanism to locally adjust the dark energy density and change the local expansion of spacetime. This idea holds tantalizing possibilities in the context of exotic spacecraft propulsion.

gr-qc↗

arXiv2009

A summation formula over the zeros of a combination of the associated Legendre functions with a physical application

By using the generalized Abel-Plana formula, we derive a summation formula for the series over the zeros of a combination of the associated Legendre functions with respect to the degree. The summation formula for the series over the zeros of the combination of the Bessel functions, previously discussed in the literature, is obtained as a limiting case. As an application we evaluate the Wightman function for a scalar field with general curvature coupling parameter in the region between concentric spherical shells on background of constant negative curvature space. For the Dirichlet boundary conditions the corresponding mode-sum contains series over the zeros of the combination of the associated Legendre functions. The application of the summation formula allows us to present the Wightman function in the form of the sum of two integrals. The first one corresponds to the Wightman function for the geometry of a single spherical shell and the second one is induced by the presence of the second shell. The boundary-induced part in the vacuum expectation value of the field squared is investigated. For points away from the boundaries the corresponding renormalization procedure is reduced to that for the boundary-free part.

math-ph↗

arXiv2009

Vacuum polarization by a cosmic string in de Sitter spacetime

In this paper we investigate the vacuum polarization effect associated with a quantum massive scalar field in a higher dimensional de Sitter spacetime in the presence of a cosmic string. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the string. So this analysis is developed by expressing the complete Wightman function as the sum of two terms: The first one corresponds to the bulk where the cosmic string is absent and the second one is induced by the presence of the string. By using the Abel-Plana summation formula, we show that for points away from the string the latter is finite at the coincidence limit and it is used to evaluate the vacuum averages of the square of the field and the energy-momentum tensor induced by the cosmic string. Simple asymptotic formulae are obtained for these expectation values for points near the string and at large distances from it. It is shown that, depending on the curvature radius of de Sitter spacetime, two regimes are realized with monotonic and oscillatory behavior of the vacuum expectation values at large distances.

hep-th↗

arXiv2009

Fermionic Casimir densities in toroidally compactified spacetimes with applications to nanotubes

Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for a massive spinor fields in higher-dimensional spacetimes with an arbitrary number of toroidally compactified spatial dimensions. By using the Abel-Plana summation formula and the zeta function technique we present the vacuum expectation values in two different forms. Applications of the general formulae to cylindrical and toroidal carbon nanotubes are given. We show that the topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications.

hep-th↗

arXiv2009

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a $(D+1)$-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.

hep-th↗

arXiv2008

Fermionic vacuum densities in higher-dimensional de Sitter spacetime

Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-dimensional de Sitter spacetimes. It is shown that, unlike to the case of 4-dimensional spacetime, for large values of the mass, these densities are suppressed exponentially. Asymptotic behavior of the topological parts in the expectation values is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological parts coincide with the corresponding quantities for a massless fermionic field and are conformally related to the corresponding flat spacetime results. In this limit the topological parts dominate the uncompactified de Sitter part and the back-reaction effects should be taken into account. In the opposite limit, for a massive field the asymptotic behavior of the topological parts is damping oscillatory.

hep-th↗

arXiv2008

Casimir densities in brane models with compact internal spaces

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional background spacetime $AdS_{D_{1}+1}\times Σ$ with a warped internal space $Σ$. The general case of different Robin coefficients on separate branes is considered. Unlike to the purely AdS bulk, the vacuum expectation values induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The brane induced parts in these expectation values vanish when the brane position tends to the AdS horizon or AdS boundary. For strong gravitational fields corresponding to large values of the AdS energy scale, the both single brane and interference parts of the expectation values integrated over the internal space are exponentially suppressed. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed. For large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane.

hep-th↗

arXiv2008

Casimir densities for wedge-shaped boundaries

The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary. In the case of the electromagnetic field perfectly conducting boundary conditions are assumed on the bounding surfaces. By using the Abel-Plana-type formula for the series over the zeros of the Bessel function, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the presence of the cylindrical shell. The additional vacuum forces acting on the wedge sides due the presence of the cylindrical boundary are evaluated and it is shown that these forces are attractive for both scalar and electromagnetic fields.

hep-th↗

arXiv2008

Coherent bremsstrahlung in periodically deformed crystals with a complex base

In the present paper we investigate coherent bremsstrahlung of high energy electrons moving in a periodically deformed single crystal with a complex base. The formula for corresponding differential cross-section is derived for an arbitrary deformation field. The conditions are discussed under which the influence of the deformation is important. The case is considered in detail when the electron enters into the crystal at small angles with respect to a crystallographic axis. It is shown that in dependence of the parameters, the presence of the deformation can either enhance or reduce the bremsstrahlung cross-section.

hep-th↗

arXiv2008

Fermionic Casimir effect in de Sitter spacetime

The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of the compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological part coincides with the corresponding quantity for a massless fermionic field and is conformally related to the corresponding flat spacetime result with the same topology. In this limit the topological term dominates the uncompactified de Sitter part and the back-reaction effects should be taken into account. In the opposite limit, for a massive field the asymptotic behavior of the topological part is damping oscillatory.

hep-th↗

arXiv2008

Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime

The vacuum expectation values of the energy--momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode-sums a variant of the generalized Abel--Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.

hep-th↗