arXiv subjects

K. V. Shajesh

Publications and source records attributed to K. V. Shajesh.

At least 37 records · Page 2Linked to original sources

arXiv2014

How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energy-momentum-stress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent ($δ$-function) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time point-split regulation parameters, and obtain well-defined contributions to the self- energy of each plate, and the interaction energy between the plates. (This self-energy does not vanish even in the conformally-coupled, strong-coupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this well-defined system is then investigated, and it is verified that the equivalence principle is satisfied.

hep-th↗

arXiv2013

Casimir interaction energies for magneto-electric δ-function plates

We present boundary conditions for the electromagnetic fields on a δ-function plate, having both electric and magnetic properties, sandwiched between two magneto-electric semi-infinite half spaces. The optical properties for an isolated δ-function plate are shown to be independent of the longitudinal material properties of the plate. The Casimir-Polder energy between an isotropically polarizable atom and a magneto-electric δ-function plate is attractive for a purely electric δ-function plate, repulsive for a purely magnetic δ-function plate, and vanishes for the simultaneous perfect conductor limit of both electric and magnetic properties of the δ-function plate. The interaction energy between two identical δ-function plates is always attractive. It can be attractive or repulsive when the plates have electric and magnetic properties interchanged and reproduces Boyer's result for the interaction energy between perfectly conducting electric and magnetic plates. The change in the Casimir-Polder energy in the presence of a δ-function plate on a magneto-electric substrate is substantial when the substrate is a weak dielectric.

hep-th↗

arXiv2013

Three-body Casimir-Polder interactions

As part of our program to develop the description of three-body effects in quantum vacuum phenomena, we study the three-body interaction of two anisotropically polarizable atoms with a perfect electrically conducting plate, a generalization of earlier work. Three- and four-scattering effects are important, and lead to nonmonotonic behavior.

quant-ph↗

arXiv2012

Electromagnetic semitransparent $δ$-function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a $δ$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $δ$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $ω_p^2=ζ_p/d$ reduces to a $δ$-function plate for frequencies ($ω=iζ$) satisfying $ζd \ll \sqrt{ζ_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $δ$-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting $δ$-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The "thick" and "thin" boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.

hep-th↗

arXiv2011

Repulsive long-range forces between anisotropic atoms and dielectrics

We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the objects is repulsive are constructed. Such configurations exist for three anisotropic atoms as well as for an anisotropic atom above a dielectric plate with a hole whose permittivity is anisotropic. Apart from the absolute magnitude of the force, the dependence on the configuration is qualitatively the same as for metallic objects for which the anisotropy is a purely geometric effect. In the weak limit closed analytic expressions for rather complicated configurations are obtained. The non-monotonic dependence of the interaction energy on separation is related to the fact that the electromagnetic Green's dyadic is not positive definite. The analysis in the weak limit is found to also semi-quantitatively explain the dependence of Casimir forces on the orientation of anisotropic dielectrics observed experimentally. Contrary to the scalar case, irreducible electromagnetic three-body energies can change sign. We trace this to the fact that the electromagnetic Green's dyadic is not positive definite.

physics.atom-ph↗

arXiv2011

Significance of many-body contributions to Casimir energies

Irreducible many-body contributions to Green's functions and Casimir energies are defined. We show that the irreducible three-body contribution to Casimir energies are significant and can be more than twenty percent of the total interaction energy. Irreducible three-body contribution for three parallel semitransparent plates in the limit when two plates overlap is obtained in terms of irreducible two-body contributions and shown to be finite and well defined in this limit.

hep-th↗

arXiv2011

Many-Body Contributions to Green's Functions and Casimir Energies

The multiple scattering formalism is used to extract irreducible N-body parts of Green's functions and Casimir energies describing the interaction of N objects that are not necessarily mutually disjoint. The irreducible N-body scattering matrix is expressed in terms of single-body transition matrices. The irreducible N-body Casimir energy is the trace of the corresponding irreducible N-body part of the Green's function. This formalism requires the solution of a set of linear integral equations. The irreducible three-body Green's function and the corresponding Casimir energy of a massless scalar field interacting with potentials are obtained and evaluated for three parallel semitransparent plates. When Dirichlet boundary conditions are imposed on a plate the Green's function and Casimir energy decouple into contributions from two disjoint regions. We also consider weakly interacting triangular--and parabolic-wedges placed atop a Dirichlet plate. The irreducible three-body Casimir energy of a triangular--and parabolic-wedge is minimal when the shorter side of the wedge is perpendicular to the Dirichlet plate. The irreducible three-body contribution to the vacuum energy is finite and positive in all the cases studied.

hep-th↗

arXiv2010

Exact Casimir energies at nonzero temperature: Validity of proximity force approximation and interaction of semitransparent spheres

In this paper, dedicated to the career of Tom Erber, we consider the Casimir interaction between weakly coupled bodies at nonzero temperature. For the case of semitransparent bodies, that is, ones described by delta-function potentials, we first examine the interaction between an infinite plane and an arbitrary curved surface. In weak coupling, such an interaction energy coincides with the exact form of the proximity force approximation obtained by summing the interaction between opposite surface elements at arbitrary temperature. This result generalizes a theorem proved recently by Decca et al. We also obtain exact closed-form results for the Casimir energy at arbitrary temperature for weakly coupled semitransparent spheres.

hep-th↗

arXiv2010

Electromagnetic Non-contact Gears: Prelude

We calculate the lateral Lifshitz force between corrugated dielectric slabs of finite thickness. Taking the thickness of the plates to infinity leads us to the lateral Lifshitz force between corrugated dielectric surfaces of infinite extent. Taking the dielectric constant to infinity leads us to the conductor limit which has been evaluated earlier in the literature.

cond-mat.other↗

arXiv2008

Lateral Casimir forces on parallel plates and concentric cylinders with corugations

In this paper we are giving a quantitative description of two different configurations for noncontact gears. We consider the solutions from a perturbative calculation for two semitransparent parallel plates and concentric cylinders both with corrugations on the inner surfaces. In the case of corrugated parallel plates we discuss results from first- and second-order perturbation calculation in the corrugation amplitudes and we will concentrate on the first-order perturbation for the case of the corrugated concentric cylinders (the second order calculation is under study), both for the weak and strong couplings. We compare the perturbative results with the results from the PFA and an exact weak coupling calculation.

hep-th↗

arXiv2008

Leading- and next-to-leading-order lateral Casimir force on corrugated surfaces

We derive explicit analytic expressions for the lateral force for two different configurations with corrugations, parallel plates and concentric cylinders. By making use of the multiple scattering formalism, we calculate the force for a scalar field under the influence of a delta-function potential that has sinusoidal dependence in one direction simulating the corrugations. By making a perturbative expansion in the amplitude of the corrugation we find the leading order for the corrugated concentric cylinders and the next-to-leading order for the corrugated parallel plates.

hep-th↗

arXiv2008

How Does Quantum Vacuum Energy Accelerate?

We show that Casimir energy for a configuration of parallel plates gravitates according to the equivalence principle both for the finite and divergent parts. This shows that the latter can be absorbed by a process of renormalization.

hep-th↗

arXiv2008

Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates

We calculate the lateral Casimir force between corrugated parallel plates, described by $δ$-function potentials, interacting through a scalar field, using the multiple scattering formalism. The contributions to the Casimir energy due to uncorrugated parallel plates is treated as a background from the outset. We derive the leading- and next-to-leading-order contribution to the lateral Casimir force for the case when the corrugation amplitudes are small in comparison to corrugation wavelengths. We present explicit results in terms of finite integrals for the case of the Dirichlet limit, and exact results for the weak-coupling limit, for the leading- and next-to-leading-orders. The correction due to the next-to-leading contribution is significant. In the weak coupling limit we calculate the lateral Casimir force exactly in terms of a single integral which we evaluate numerically. Exact results for the case of the weak limit allows us to estimate the error in the perturbative results. We show that the error in the lateral Casimir force, in the weak coupling limit, when the next-to-leading order contribution is included is remarkably low when the corrugation amplitudes are small in comparison to corrugation wavelengths. We expect similar conclusions to hold for the Dirichlet case. The analogous calculation for the electromagnetic case should reduce the theoretical error sufficiently for comparison with the experiments.

hep-th↗

arXiv2008

Non-contact gears: II. Casimir torque between concentric corrugated cylinders for the scalar case

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for non-contact gears. To this end, we calculate the Casimir torque between two such cylinders, described by $δ$-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.

hep-th↗

arXiv2007

PT-Symmetry Quantum Electrodynamics--PTQED

The construction of $\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.

hep-th↗

arXiv2007

How does Casimir energy fall? III. Inertial forces on vacuum energy

We have recently demonstrated that Casimir energy due to parallel plates, including its divergent parts, falls like conventional mass in a weak gravitational field. The divergent parts were suitably interpreted as renormalizing the bare masses of the plates. Here we corroborate our result regarding the inertial nature of Casimir energy by calculating the centripetal force on a Casimir apparatus rotating with constant angular speed. We show that the centripetal force is independent of the orientation of the Casimir apparatus in a frame whose origin is at the center of inertia of the apparatus.

hep-th↗

arXiv2007

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here add further support to this conclusion by considering parallel semitransparent plates, that is, delta-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (tau,x,y,xi). Fixed xi in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of xi. In the limit of large Rindler coordinate xi (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just Mg, where g is the gravitational acceleration and M is the total mass of the system, consisting of the mass of the plates renormalized by the Casimir energy of each plate separately, plus the energy of the Casimir interaction between the plates. This reproduces the previous result in the limit as the coupling to the delta-function potential approaches infinity.

hep-th↗

arXiv2007

How Does Casimir Energy Fall?

Doubt continues to linger over the reality of quantum vacuum energy. There is some question whether fluctuating fields gravitate at all, or do so anomalously. Here we show that for the simple case of parallel conducting plates, the associated Casimir energy gravitates just as required by the equivalence principle, and that therefore the inertial and gravitational masses of a system possessing Casimir energy $E_c$ are both $E_c/c^2$. This simple result disproves recent claims in the literature. We clarify some pitfalls in the calculation that can lead to spurious dependences on coordinate system.

hep-th↗