Prachi Parashar

Repulsive Casimir and Casimir–Polder forces

Casimir and Casimir?Polder repulsions have been known for more than 50 years. The general ?Lifshitz? configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso?s group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on some recent developments will be surveyed. Here, stress will be placed on analytic developments, especially on Casimir?Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker?s 75th birthday devoted to ?Applications of zeta functions and other spectral functions in mathematics and physics?.

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

Exact results for Casimir interactions between dielectric bodies: the weak-coupling or van der Waals limit.

{E}_{c}

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

are both

Noncontact gears. II. Casimir torque between concentric corrugated cylinders for the scalar case

{E}_{c}/{c}^{2}

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

. This simple result disproves recent claims in the literature. We clarify some pitfalls in the calculation that can lead to spurious dependences on the coordinate system.

Gravitational and inertial mass of Casimir energy

In earlier papers, we have applied multiple-scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again, exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres, between cylinders, and between an infinite plate and a rectangular slab of finite size. For such a slab, we consider the torque acting on it and find that nontrivial equilibrium points can occur.

How does Casimir energy fall? IV. Gravitational interaction of regularized 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, ?-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (?, x, y, ?). Fixed ? in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of ?. In the limit of a large Rindler coordinate ? (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 ?-function potential approaches infinity.

Multiple Scattering Casimir Force Calculations: Layered and Corrugated Materials, Wedges, and Casimir-Polder Forces

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for noncontact gears. To this end, we calculate the Casimir torque between two such cylinders, described by {delta}-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.

Casimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids

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.