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Let $(U_t)_{t \geq 0}$ be a Brownian motion valued in the complex projective space $\mathbb{C}P^{N-1}$. Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of $|U_t^{1}|^2$ and of $(|U_t^{1}|^2,…
The calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum $J$ is a good quantum number. One goal of…
An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters…
In the present work an attempt has been made to study the dynamics of a diatomic molecule N2 in water. The proposed model consists of Langevin stochastic differential equation whose solution is obtained through Euler's method. The proposed…
A two-electron one-dimensional model of a heteroatomic molecule composed of two open-shell atoms is considered. Including only two electrons isolates and examines the effect that the highest occupied molecular orbital has on the Kohn-Sham…
This paper is the second in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian gravity and general relativity. In this second paper we develop the Newtonian theory, inspired…
Using the Hugenholtz-Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of single-nucleon potentials in isospin asymmetric nuclear matter. These analytical relations are useful for…
A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…
In this study, we present a quantum-statistical analysis of H$_2$ and LiH diatomic molecules within the Frost--Musulin potential framework. By combining the analytical bound-state approach to the radial Schr\"odinger problem with the…
We propose a highly efficient and fast method of translational cooling for high-angular-momentum atoms. Optical pumping and stimulated transitions, combined with magnetic forces, can be used to compress phase-space density, and the…
Emission from the pure rotational transitions of H$_2$ traces warm molecular gas, providing insight into its temperature distribution and local heating conditions. We have extended previous power-law H$_2$ temperature models to account for…
The hydroxyl radical, hereafter referred to as the OH molecule (OHM), carries both electric and magnetic dipole moments and, as a diatomic molecule, admits a comparatively simple and accurate model. This makes it a natural quantum probe for…
In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Ho\v{r}ava gravity and Einstein-aether theory. We assume a specific non-static configuration of the aether vector field and…
We study a $PT$-symmetric quantum mechanical model with an O(N)-symmetric potential of the form $m^{2}\vec{x}^{2}/2-g(\vec{x}^{2})^{2}/N$ using its equivalent Hermitian form. Although the corresponding classical model has finite-energy…
We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspects induced. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in…
In this work, we study the nematic-isotropic phase transition based on the dynamics of the Landau--De Gennes theory of liquid crystals. At the critical temperature, the Landau--De Gennes bulk potential favors the isotropic phase and nematic…
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
It is known that the asymptotic decay of the electron density $n(\br)$ outside a molecule is informative about its first ionization potential $I_0$, $n(|\br|\to\infty) \sim \text{exp}(-2\sqrt{2I_0}\,r)$. This dictates the orbital energy of…