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The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron oscillation through the nuclei of H2+ accounts for…
A non-moving electron hydrogen model is proposed, resolving a long standing contradiction (94 years) in the hydrogen atom. This, however, forces to not use the "in an orbit point particle kinetic energy" as the phenomenon responsible for…
Using explicit solutions of the QCD transport equations, we construct an effective potential for an anisotropic quark-gluon plasma which under plausible assumptions holds beyond the Hard Loop approximation. The configurations, which are…
In quantum dots or molecules with vibrational degrees of freedom the electron-vibron coupling renormalizes the electronic charging energy. For sufficiently strong coupling, the renormalized charging energy can become negative. Here, we…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…
A chiral 4-fermion or 4-unit charge Coulomb structure for perturbed atom H implies that an intra-atomic H-Hbar transition must obey the same quantitative criteria as a classical intra-molecular Walden inversion. In a trigonal pyramid model…
We consider configurations of $N$ charged particles on the interval with nearest neighbour Coulomb interaction and constant external force. For different values of external force we find 4 different phases of the asymptotic particle density…
Noncommutative algebra which is rotationally invariant, time reversal invariant and equivalent to noncommutative algebra of canonical type is considered. Perihelion shift of orbit of a particle in Coulomb potential in the…
We have constructed the appropriate Hamiltonian of the noncommutative coulombic monopole (i.e. the noncommutative hydrogen atom with a monopole). The energy levels of this system have been calculated, discussed and compared with the…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
The $(p,d,\bar{p},\bar{d})$ molecule, with a proton, a deuteron and their antiparticles, is stable againt spontaneous dissociation, but none of its three-body subsystems are stable. This molecule should be built by combining two atoms, for…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…
This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…
It is known that homogeneous distribution of particles in Coulomb-like systems can be unstable, and spatially inhomogeneous structures can be formed. A simple method for describing such inhomogeneous systems and obtaining spacial…
Quadratic gravity is a UV completion of general relativity, which also solves the hierarchy problem. The presence of 4 derivatives implies via the Ostrogradsky theorem that the $classical$ Hamiltonian is unbounded from below. Here we solve…
We studied the instability of the regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes under charged scalar perturbations. The unstable modes satisfy the superradiant condition, but not all modes satisfying the superradiant…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…