Casimir interactions of an object inside a spherical metal shell

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.Comment: 4 pages, 3 figure

Casimir potential of a compact object enclosed by a spherical cavity

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.Comment: 12 pages, 6 figure

Casimir Force at a Knife's Edge

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.Comment: 5 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no changes to results); v4: fix similar factor in Eq. (16) (again no changes to results

Casimir spring and compass: Stable levitation and alignment of compact objects

We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium can be predicted based on the sign of the force, but the torque cannot be.Comment: 5 pages, 4 figure

Classical Casimir interaction in the plane-sphere geometry

We study the Casimir interaction in the plane-sphere geometry in the classical limit of high temperatures. In this limit, the finite conductivity of the metallic plates needs to be taken into account. For the Drude model, the classical Casimir interaction is nevertheless found to be independent of the conductivity so that it can be described by a single universal function depending only on the aspect ratio $x=L/R$ where $L$ is the interplate distance and $R$ the sphere radius. This universal function differs from the one found for perfect reflectors and is in principle amenable to experimental tests. The asymptotic approach of the exact result to the Proximity Force Approximation appears to be well fitted by polynomial expansions in $\ln x$.Comment: Updated version with minor modifications and addition of a referenc

Fluctuation induced quantum interactions between compact objects and a plane mirror

The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.Comment: 19 pages, 7 figure

Geometry and material effects in Casimir physics - Scattering theory

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.Comment: 44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics volume in Casimir physic

Casimir forces between arbitrary compact objects: Scalar and electromagnetic field

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As examples, we obtain this series for two spheres with Robin boundary conditions for a scalar field and dielectric spheres for the electromagnetic field. The full interaction at all separations is obtained for spheres with Robin boundary conditions and for perfectly conducting spheres.Comment: 24 pages, 3 figures, contribution to QFEXT07 proceeding

Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study

PURPOSE: To report the methodology and findings of a large scale investigation of burden and distribution of refractive error, from a contemporary and ethnically diverse study of health and disease in adults, in the UK.METHODS:U K Biobank, a unique contemporary resource for the study of health and disease, recruited more than half a million people aged 40-69 years. A subsample of 107,452 subjects undertook an enhanced ophthalmic examination which provided autorefraction data (a measure of refractive error). Refractive error status was categorised using the mean spherical equivalent refraction measure. Information on socio-demographic factors (age, gender, ethnicity, educational qualifications and accommodation tenure) was reported at the time of recruitment by questionnaire and face-to-face interview.RESULTS: Fifty four percent of participants aged 40-69 years had refractive error. Specifically 27% had myopia (4% high myopia), which was more common amongst younger people, those of higher socio-economic status, higher educational attainment, or of White or Chinese ethnicity. The frequency of hypermetropia increased with age (7% at 40-44 years increasing to 46% at 65-69 years), was higher in women and its severity was associated with ethnicity (moderate or high hypermetropia at least 30% less likely in non-White ethnic groups compared to White).CONCLUSIONS: Refractive error is a significant public health issue for the UK and this study provides contemporary data on adults for planning services, health economic modelling and monitoring of secular trends. Further investigation of risk factors is necessary to inform strategies for prevention. There is scope to do this through the planned longitudinal extension of the UK Biobank study

Temporal trends in frequency, type and severity of myopia and associations with key environmental risk factors in the UK: Findings from the UK Biobank Study

This study investigated temporal trends in the epidemiology of primary myopia and associations with key environmental risk factors in a UK population. Data were collected at recruitment (non-cycloplegic autorefraction, year of birth, sex, ethnicity, highest educational attainment, reason and age of first wearing glasses and history of eye disease) from 107,442 UK Biobank study participants aged 40 to 69 years, born between 1939 and 1970. Myopia was defined as mean spherical equivalent (MSE) ≤-1 dioptre (D). Temporal changes in myopia frequency by birth cohort (5-year bands using date of birth) and associations with environmental factors were analysed, distinguishing both type (childhood-onset, <18 years versus adult-onset) and severity (three categories: low -1.00 to -2.99D, moderate -3.00 to -5.99D or high ≥-6.00D). Overall myopia frequency increased from 20.0% in the oldest cohort (births 1939-1944) to 29.2% in the youngest (1965-1970), reflecting a relatively higher increase in frequency of adult-onset and low myopia. Childhood-onset myopia peaked in participants born in 1950-54, adult-onset myopia peaked in the cohort born a decade later. The distribution of MSE only shifted for childhood-onset myopia (median: -3.8 [IQR -2.4, -5.4] to -4.4 [IQR -3.0, -6.2]). The magnitude of the association between higher educational attainment (proxy for educational intensity) and myopia overall increased over time (adjusted Odds Ratio (OR) 2.7 [2.5, 2.9] in the oldest versus 4.2 [3.3, 5.2] in the youngest cohort), being substantially greater for childhood-onset myopia (OR 3.3 [2.8, 4.0] to 8.0 [4.2, 13]). Without delineating childhood-onset from adult-onset myopia, important temporal trends would have been obscured. The differential impact of educational experience/intensity on both childhood-onset and high myopia, amplified over time, suggests a cohort effect in gene-environment interaction with potential for increasing myopia frequency if increasing childhood educational intensity is unchecked. However, historical plateauing of myopia frequency does suggest some potential for effective intervention