Related papers: On the corrections beyond proximity force approxim…
We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different…
We compute bounds and forecasts on screened modified gravity theories, specialising to the chameleon model in Casimir force experiments. In particular, we investigate the classical interaction between a plate and sphere subject to a…
We calculate the Casimir force and its gradient between a spherical and a planar gold surface. Significant numerical improvements allow us to extend the range of accessible parameters into the experimental regime. We compare our numerically…
We compute the first radiative correction to the Casimir energy of a massive scalar field with a quartic self-interaction in the presence of two parallel plates. Three kinds of boundary conditions are considered: Dirichlet-Dirichlet,…
We consider the small separation asymptotic expansions of the Casimir interaction energy and the Casimir interaction force between two parallel cylinders. The leading order terms and the next-to-leading order terms are computed…
A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett {\bf 120}, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres in vacuum at room temperature, and…
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…
We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from…
We analyze the possibility to measure small thermal effects in the Casimir force between metal test bodies in configurations of a sphere above a plate and two parallel plates. For sphere-plate geometry used in many experiments we…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
We analyze recent experiments on measuring the thermal Casimir force with account of possible background effects. Special attention is paid to the validity of the proximity force approximation (PFA) used in the comparison between the…
Let $\tau_k(\Omega)$ be the $k$-th eigenvalue of the Laplace operator in a bounded domain $\Omega$ of the form $\Omega_{\text{out}} \setminus \overline{B_{\alpha}}$ under the Neumann boundary condition on $\partial \Omega_{\text{out}}$ and…
This article is the continuation of our first work on the determination of the cases where there is equality in Courant's Nodal Domain theorem in the case of a Robin boundary condition (with Robin parameter $h$). For the square, our first…
The lateral Casimir force between two corrugated metallic plates makes possible a study of the nontrivial interplay of geometry and Casimir effect appearing beyond the regime of validity of the Proximity Force Approximation (PFA).…
We consider the eigenvalues of the Laplacian on an open, bounded, connected set in $\mathbb{R}^n$ with $C^2$ boundary, with a Neumann boundary condition or a Robin boundary condition. We obtain upper bounds for those eigenvalues that have a…
Using a path integral approach we rederive a recently found representation of the Casimir energy for a sphere and a cylinder in front of a plane and derive the first correction to the proximity force theorem.
The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of…
In this paper aiming to obtain the Casimir energy between a sinusoidally corrugated sphere and a plate, we first present a derivation of the sphere-plate Casimir force obtained by applying proximity force approximation (PFA). One may…
We argue that the appropriate variable to study a non trivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the…
We apply a perturbative approach to evaluate the Casimir energy for a massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary conditions on two surfaces. One of the surfaces is assumed to be flat, while the other…