Giuseppe Bimonte

Casimir forces beyond the proximity approximation

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Pade extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere/plate Casimir force at all separations.

Material dependence of Casimir forces: Gradient expansion beyond proximity

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here, we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room temperature. We derive an explicit expression for the amplitude θ1 of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, θ1 has an unusually large temperature dependence.

Towards measuring variations of Casimir energy by a superconducting cavity.

We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and this gives rise to a number of testable effects, including a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The theoretical ground is therefore prepared for the first experiment ever aimed at measuring variations of the Casimir energy itself.

Relativistic mechanics of Casimir apparatuses in a weak gravitational field

This paper derives a set of general relativistic cardinal equations for the equilibrium of an extended body in a uniform gravitational field. These equations are essential for a proper understanding of the mechanics of suspended relativistic systems. As an example, the prototypical case of a suspended vessel filled with radiation is discussed. The mechanics of Casimir apparatuses at rest in the gravitational field of the Earth is then considered. Starting from an expression for the Casimir energy-momentum tensor in a weak gravitational field recently derived by the authors, it is shown here that, in the case of a rigid cavity supported by a stiff mount, the weight of the Casimir energy E c stored in the cavity corresponds to a gravitational mass M = E c /c 2 , in agreement with the covariant conservation law of the regularized energy-momentum tensor. The case of a cavity consisting of two disconnected plates supported by separate mounts, where the two measured forces cannot be obtained by straightforward arguments, is also discussed.

Non-equilibrium Casimir forces: Spheres and sphere-plate

We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.

From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field

This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration g, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gravity acceleration g. The general structure of the calculation is therefore elucidated, and the components of the Maxwell energy-momentum tensor are evaluated up to second order in g, improving a previous analysis by the authors and correcting their old first-order formula for the Casimir energy.

Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry.

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.

Peierls Brackets in Field Theory

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.

A Theory of Electromagnetic Fluctuations for Metallic Surfaces and van der Waals Interactions between Metallic Bodies

A new general expression is derived for the fluctuating electromagnetic field outside a metal surface in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between dielectric solids. The theory is used to compute the radiative heat transfer between two parallel metal surfaces at different temperatures. It is shown that a measurement of this quantity may provide an experimental resolution of a long-standing controversy about the effect of thermal corrections on the Casimir force between real metal plates.

Variations of Casimir energy from a superconducting transition

Abstract We consider a five-layer Casimir cavity, including a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the microwave region) of the reflection coefficient of the film produces a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and thus causes a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The proposed scheme might also help clarifying the current controversy about the magnitude of the contribution to Casimir free energy from the TE zero mode, as we find that alternative treatments of this mode strongly affect the shift of critical field.