Related papers: Van der Waals interactions between two hydrogen at…
We show that the asymptotic formula for $\pi$, the Wallis formula, that was related with quantum mechanics and the hydrogen atom in \cite{HF}, can also be related to the harmonic oscillator using a quantum duality between these two systems.…
Neutral atoms interact through a van der Waals potential which asymptotically falls off as r^{-6}. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise…
We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are…
It can be fruitful to view two-component physical systems of attractive monomers, A and B, ``chemically'' in terms of a reaction A + B <-> C, where C = AB is an associated pair or complex. We show how to construct free energies in the…
A simple theory is proposed for the dispersive molecular binding of unusually high magnitude due to an enhanced polarizability. Two alternative ways have so far been considered in the literature leading to the polarizability enhancement:…
The atomic dipole polarizability, $\alpha$, and the van der Waals (vdW) radius, $R_{\rm vdW}$, are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently…
We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $\alpha \to 0$ together with the relative distance between the atoms increasing as $\alpha^{-\gamma} R$, $\gamma > 0$.…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
We extend the Van der Waals equation of state to a universal form and find that the van der Waals equation of state is a special condition of this form. Then a good form of the equation of state for a balanced liquid-gas coexistence…
The paper discusses a model of Van der Waals crystals in which band-gap structures do not form. An effect of strong and chaotic electron-electron repulsion, which was excluded from consideration in the traditional approach, is taken into…
We show that the viscous Camassa-Holm equation subject to an external force, and where the viscosity term is given by second order differential operator in divergence form has a global attractors in the energy space $H^1$. Moreover, we…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when…
The relaxation dynamics in two van der Waals bonded and one hydrogen-bonding molecular liquids is studied as a function of pressure and temperature by incoherent neutron scattering using simultaneous dielectric spectroscopy. The dynamics is…
The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of $e-\rm H_2$ interaction. Within a cluster virial expansion, the Beth-Uhlenbeck formula is applied to infer the contribution…
The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic $C_6$ coefficients characterizing the van der…
We aim to understand how the van der Waals force between neutral adatoms and a graphene layer is modified by uniaxial strain and electron correlation effects. A detailed analysis is presented for three atoms (He, H, and Na) and graphene…
The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient…
We studied the van der Waals interactions of two finite, solid, cylindrical rods at arbitrary angle and position with respect to each other. An analytic interpolative formula for the interaction potential energy is constructed, based on…
We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei together with the Coulomb interaction between the electrons can be approximated by harmonic…