Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

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 and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.Comment: 4 pages, 3 figure

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.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding

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.Comment: 5 pages, 1 figure, REVTeX. Minor revisions, including changes in reference

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

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

We derive boundary conditions for electromagnetic fields on a $\delta$-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 $\delta$-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 $\omega_p^2=\zeta_p/d$ reduces to a $\delta$-function plate for frequencies ($\omega=i\zeta$) satisfying $\zeta d \ll \sqrt{\zeta_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $\delta$-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 $\delta$-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.Comment: 21 pages, 7 figures, references adde

Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schr\"odinger equation

The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h_6 and its associated quantum universal R-matrix. A deformed one-boson representation for this algebra is deduced and applied to construct a first order deformation of the differential equation that generates the two-photon algebra eigenstates in Quantum Optics. On the other hand, the isomorphism between h_6 and the (1+1) Schr\"odinger algebra leads to a new quantum deformation for the latter for which a differential-difference realization is presented. From it, a time discretization of the heat-Schr\"odinger equation is obtained and the quantum Schr\"odinger generators are shown to be symmetry operators.Comment: 12 pages, LaTe

Geometric discord and Measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.Comment: V2: Title changed, one more state added; 11 pages (single column), 2 figures, accepted in Quantum Information Processin

Household Transmission of Rotavirus in a Community with Rotavirus Vaccination in Quininde, Ecuador

Background: We studied the transmission of rotavirus infection in households in peri-urban Ecuador in the vaccination era. Methods: Stool samples were collected from household contacts of child rotavirus cases, diarrhea controls and healthy controls following presentation of the index child to health facilities. Rotavirus infection status of contacts was determined by RT-qPCR. We examined factors associated with transmissibility (index-case characteristics) and susceptibility (householdcontact characteristics). Results: Amongst cases, diarrhea controls and healthy control household contacts, infection attack rates (iAR) were 55%, 8% and 2%, (n = 137, 130, 137) respectively. iARs were higher from index cases with vomiting, and amongst siblings. Disease ARs were higher when the index child was ,18 months and had vomiting, with household contact ,10 years and those sharing a room with the index case being more susceptible. We found no evidence of asymptomatic infections leading to disease transmission. Conclusion: Transmission rates of rotavirus are high in households with an infected child, while background infections are rare. We have identified factors associated with transmission (vomiting/young age of index case) and susceptibility (young age/sharing a room/being a sibling of the index case). Vaccination may lead to indirect benefits by averting episodes or reducing symptoms in vaccinees

(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups

All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrodinger Poisson-Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and gl(2) Lie bialgebras within the Schrodinger classification are studied. As an application, new quantum (Hopf algebra) deformations of the Schrodinger algebra, including their corresponding quantum universal R-matrices, are constructed.Comment: 25 pages, LaTeX. Possible applications in relation with integrable systems are pointed; new references adde

Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.