Hide it to see it better: a robust setup to probe the thermal Casimir effect

We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of which is "hidden" by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass filter that allows for a clean observation of the controversial thermal Casimir force between the corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that have been proposed in the literature for the thermal Casimir effect.Comment: 5 pages, 2 encapsulated figures, final version accepted for publication in Physical Review Letter

Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions

Exploiting conformal symmetry, we derive a simple exact formula for the classical electromagnetic Casimir interaction of two perfectly conducting three-spheres, including the sphere-plate geometry as a special case, in four euclidean dimensions. We verify that the short distance expansion of the Casimir energy agrees to leading order with the Proximity Force Approximation (PFA), while the next-to-leading-order is in agreement with a recently proposed derivative expansion of the Casimir energy. At the next-to-next-to-leading order we find a non-analytic correction to PFA, which for a sphere-plate system is of the order of $(d/R)^{3/2} \log(d/R)$, where $d$ is the separation and $R$ the sphere radius.Comment: 19 pages, 2 figure

Observing the Casimir-Lifshitz Force Out of Thermal Equilibrium

The thermal Casimir-Lifshitz force among two bodies held at different temperatures displays striking features that are absent in systems in thermal equilibrium. The manifestation of this force has been observed so far only in Bose-Einstein condensates close to a heated substrate, but never between two macroscopic bodies. Observation of the thermal Casimir-Lifhitz force out of thermal equilibrium with conventional Casimir setups is very difficult, because for experimentally accessible separations the thermal force is small compared to the zero-temperature quantum Casimir force, unless prohibitively large temperature differences among the plates are considered. We describe an apparatus that allows for a direct observation of the thermal force out of equilibrium for submicron separations and for moderate temperature differences between the plates.Comment: 5 pages, 3 encapsulated figure

Comment on " Low-frequency character of the Casimir force between metallic films"

In Phys. Rev. {\bf E 70}, 047102 (2004), J.R. Torgerson and S.K. Lamoreaux investigated for the first time the real-frequency spectrum of finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid. However, their analysis of the problem, based on more appropriate low-frequency metallic boundary conditions, uses an incorrect form of boundary conditions for TE modes. We repeat their analysis, using the correct boundary conditions. Our computations confirm their most important result: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The magnitude of the correction has a value about twenty times larger than that quoted by them.Comment: 3 pages, 2 figures. In press on Phys. Rev.

Apparatus to probe the influence on the Casimir effect of the Mott-Anderson metal-insulator transition in doped semiconductors

We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of sub-micron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of error that blur the interpretation of Casimir experiments, like electrostatic patches, inaccurate determination of plates separation, surface roughness and errors in the optical data. With the help of the proposed setup it should be possible to establish conclusively which among the alternative theories of the Casimir effect for semiconducting test bodies is correct.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.

Wave-scattering from a gently curved surface

We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.Comment: 5 pages, accepted for publication in Phys. Lett.

Classical brackets for dissipative systems

We show how to write a set of brackets for the Langevin equation, describing the dissipative motion of a classical particle, subject to external random forces. The method does not rely on an action principle, and is based solely on the phenomenological description of the dissipative dynamics as given by the Langevin equation. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism.Comment: Latex file, 8 pages, prepared for the Conference Spacetime and Fundamental Interactions: Quantum Aspects, Vietri sul Mare, Italy, 26-31 May 200

New classical brackets for dissipative systems

A set of brackets for classical dissipative systems, subject to external random forces, are derived. The method is inspired to the old procedure found by Peierls, for deriving the canonical brackets of conservative systems, starting from an action principle. It is found that an adaptation of Peierls' method is applicable also to dissipative systems, when the friction term can be described by a linear functional of the coordinates, as is the case in the classical Langevin equation, with an arbitrary memory function. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism.Comment: 4 page

Casimir--Polder force between anisotropic nanoparticles and gently curved surfaces

The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.Comment: 9 pages, 10 encapsulated figure