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Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction…

We obtain analytically the exact non-retarded dispersive interaction energy between an atom and a perfectly conducting disc. We consider the atom in the symmetry axis of the disc and assume the atom is predominantly polarizable in the…

Using fourth-order perturbation theory, a general formula for the van der Waals potential of two neutral, unpolarized, ground-state atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is…

We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient…

We calculate the van der Waals dispersive interaction between a neutral but polarizable atom and a perfectly conducting isolated sphere in the nonretarded case. We make use of two separate models, one being the semiclassical…

Within the frame of macroscopic quantum electrodynamics in causal media, the van der Waals interaction between an atomic system and an arbitrary arrangement of dispersing and absorbing dielectric bodies including metals is studied. It is…

A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld…

Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…

The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material,…

The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…

We consider a molecule in the Born-Oppenheimer approximation interacting with a plate of infinite thickness, i.e, a half--space, which is perfectly conducting or dielectric. It is well--known in the physics literature that in this case the…

The method recently developed to include Van der Waals interactions in the Density Functional Theory by using the Maximally-Localized Wannier functions, is improved and extended to the case of atoms and fragments weakly bonded (physisorbed)…

A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…

A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…

Within the framework of macroscopic quantum electrodynamics, the resonant van der Waals potential experienced by an excited two-level atom near a planar magneto-electric two-layer system consisting of a slab of left-handed material and a…

We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of…

We consider potential-based interactions between beams (or fibers) and shells (or membranes) using a coarse-grained approach with focus on van der Waals attraction and steric repulsion. The involved 6D integral over volumes of a beam and a…

Diffraction of a surface wave on a rectangular wedge with impedance faces is studied using the Sommerfeld-Malyuzhinets technique. An analog of Landau's bypass rule in the theory of plasma waves is introduced for selection of a correct…

The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…

We extend a method (E. Canc\`es and L.R. Scott, SIAM J. Math. Anal., 50, 2018, 381--410) to compute more terms in the asymptotic expansion of the van der Waals attraction between two hydrogen atoms. These terms are obtained by solving a set…