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The variational argument is presented to establish the attainability of homogeneity of degree one in the number of particles for any functional $F[n, f]$ that depends on both the state variable $f$ and the particle count $n$. Euler's…
We study the effect of a hidden gauge symmetry on complex holomorphic systems. For this purpose, we show that intrinsically any holomorphic system has this gauge symmetry. We establish that this symmetry is related to the Cauchy-Riemann…
Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid-fluid phase transition in…
The one dimensional Schroedinger hydrogen atom is an interesting mathematical and physical problem to study bound states, eigenfunctions and quantum degeneracy issues. This 1D physical system gave rise to some intriguing controversy over…
Path integral Monte Carlo simulations are applied to study dense atomic hydrogen in the regime where the protons form a Wigner crystal. The interaction of the protons with the degenerate electron gas is modeled by Thomas-Fermi screening,…
Hydrogen incorporation in native surface oxides of metal alloys often controls the onset of metal hydriding, with implications for materials corrosion and hydrogen storage. A key representative example is titania, which forms as a…
We scrutinize the behaviour of hydrogen atom's eigenvalues in a quantum plasma as it interacts with electric field directed along $\theta=\pi$ and exposed to linearly polarized intense laser field radiation. Using the Kramers-Henneberger…
Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in…
For a two-phase (liquid-gas) two-component (water-hydrogen) system in porous media we discuss the formulation of the possible dissolution of hydrogen in the liquid phase. We show how Henry's law fits in a phase diagram. Then the problem is…
The search for the weakly-coupled Higgs sector at future colliders consists of three phases: discovery of a Higgs candidate, verification of the Higgs interpretation of the signal, and precision measurements of Higgs sector properties. The…
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in…
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.…
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…
By using a step-like potential, it is possible to mimic the Rydberg short range part of the interaction between two atoms. It is easy in this case to establish an analytical solution of the Schr\"{o}dinger equation. In this contribution, we…
Relative hadron abundances from high-energy heavy-ion collisions reveal substantial inhomogeneities of temperature and baryon-chemical potential within the decoupling volume. The freeze-out volume is not perfectly "stirred", i.e. the…
The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal…
A powerful method of manipulating the dynamics of quantum coherent particles is to control the phase of their tunneling. We consider a system of two electrons hopping on a quasi one-dimensional lattice in the presence of a uniform magnetic…
In a recent paper, it has been shown the Schr\"{o}dinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformation. Here, it is demonstrated that the same…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications…