A New Relativistic Model for Polyatomic Gases Interacting with an Electromagnetic Field

Maxwell’s equations in materials are studied jointly with Euler equations using new knowledge recently appeared in the literature for polyatomic gases. For this purpose, a supplementary conservation law is imposed; one of the results is a restriction on the law linking the magnetic field in empty space and the electric field in materials to the densities of the 4-Lorentz force να and its dual μα: These are the derivatives of a scalar function with respect to να and μα, respectively. Obviously, two of Maxwell’s equations are not evolutive (Gauss’s magnetic and electric laws); to simplify this mathematical problem, a new symmetric hyperbolic set of equations is here presented which uses unconstrained variables and the solutions of the new set of equations, with initial conditions satisfying the constraints, restore the previous constrained set. This is also useful because it allows to maintain an overt covariance that would be lost if the constraints were considered from the beginning. This is also useful because in this way the whole set of equations becomes a symmetric hyperbolic system as usually in Extended Thermodynamics.

Non-relativistic Quark Model under External Magnetic and Aharanov-Bohm (AB) Fields in the Presence of Temperature-Dependent Confined Cornell Potential

The dissociation of quarkonia in a thermal QCD medium in the background of an AB and strong magnetic fields is investigated. For this purpose, the Schrödinger equation with a charged quarkonium in the Cornell potential under the influence of AB flux and an external magnetic fields directed along the z-axis is employed. By using the Nikiforov-Uvarov (NU) method, the energy eigenvalue is obtained. The effect of temperature, AB flux, and an external magnetic field is studied. The study shows that the dissociation energy of 1S states of charmonium and bottomonium decreases with increasing temperature and AB flux, and external magnetic field. Also, the quarkonium melts faster in a hot medium in the presence of AB flux and external magnetic field. We found that the charmonium melts at 13.79 m²_πGeV² and the bottomonium melts at 99.48 m²_πGeV² . A comparison is studied with other works. Thus, the present non-relativistic model gives satisfactory results for dissociation binding energy in a hot medium when AB flux and external magnetic fields are included.