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.
We present a detailed derivation of heat radiation, heat transfer, and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The ...results can be expressed as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that is not due to radiation pressure.
Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or ...high-temperature limit of Casimir interactions between two spheres (interior and exterior configurations), including the sphere-plane geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary conditions and metallic boundary conditions described by the Drude model. At short distances, closed-form expansions are derived from the exact result, displaying an intricate structure of deviations from the commonly employed proximity force approximation.
The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to ...compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.
A recent experiment J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 120, 040401 (2018) measured for the first time the gradient of the Casimir force between two gold spheres in ...vacuum at room temperature, and placed a bound on the magnitude of the deviation of the measured force from the proximity force approximation (PFA). The present work extends a previous theoretical analysis of this experiment G. Bimonte, Phys. Rev. D 97, 085011 (2018), by analyzing in detail how the magnitude of the deviation from PFA is affected by the inclusion or neglect of ohmic dissipation at zero frequency, a much debated issue in the current Casimir literature, which goes by the name of the Drude vs plasma controversy. We analyze as well the effect of connecting the conductors to charge reservoirs, which is the standard configuration used in Casimir experiments. We describe a simple and effective decimation procedure, allowing for a faster computation of the Casimir force for large aspect ratios of the system.
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.
The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge, ...dimension of a boundary changing operator), along with the solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium is demonstrated for certain conformally invariant models, including the tricritical Ising model.
A recent experiment J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett. 120, 040401 (2018) measured for the first time the gradient of the Casimir force between two gold spheres at ...room temperature. The theoretical analysis of the data was carried out using the standard proximity force approximation (PFA). A fit of the data, using a parametrization of the force valid for the sphere-plate geometry, was used by the authors to place a bound on deviations from PFA. Motivated by this work, we compute the Casimir force between two gold spheres at finite temperature. The semianalytic formula for the Casimir force that we construct is valid for all separations, and can be easily used to interpret future experiments in both the sphere-plate and sphere-sphere configurations. We describe the correct parametrization of the corrections to PFA for two spheres that should be used in data analysis.
We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) ...Si, and the other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer, covering both regions. The setup offers two important advantages over existing Casimir setups. On one hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
PDF
