Related papers: High Energy Dirac Solutions: Issues and Ramificati…
Ten new exact solutions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The solutions are obtained by assuming certain relations among the coefficients $a(x)$, $b(x)$ and $c(x)$ of the Riccati equation, in the form of…
Two approaches to calculations' minimization in High Energy Physics are considered. The first one is the method of covariant calculations for the amplitudes of processes with polarized Dirac particles. The second one connects with the…
Recent data from the Pierre Auger Observatory has revealed the presence of a large-scale dipole in the arrival direction distribution of ultra-high energy cosmic rays (UHECR). In this work, we build up an understanding of the diffusive…
Resonance fluorescence of laser-driven highly charged ions is studied in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for…
A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones…
All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation.…
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy…
We give a detailed study of the infinite-energy solutions of the Cahn-Hilliard equation in the 3D cylindrical domains in uniformly local phase space. In particular, we establish the well-posedness and dissipativity for the case of regular…
The origin of cosmic rays is one of the major unresolved questions in astrophysics. In particular, the highest energy cosmic rays observed possess macroscopic energies and their origin is likely associated with the most energetic processes…
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
The highest energy cosmic rays observed possess macroscopic energies and their origin is likely to be associated with the most energetic processes in the Universe. Their existence triggered a flurry of theoretical explanations ranging from…
Energy distributions of decay products carry information on the kinematics of the decay in ways that are at the same time straightforward and quite hidden. I will review these properties and discuss their early historical applications as…
We discuss the basic difficulties in understanding the origin of the highest energy particles in the Universe - the ultrahigh energy cosmic rays (UHECR). It is difficult to imagine the sources they are accelerated in. Because of the strong…
There are several mathematical and physical reasons why Dirac's quantization must hold. How far one can go without it remains an open problem. The present work outlines a few steps in this direction.
Mathematical ideas and approaches common in complexity-related fields have been fruitfully applied in experimental high energy physics also. We briefly review some of the cross-pollination that is occurring.
The origin of cosmic rays is one of the major unresolved astrophysical questions. In particular, the highest energy cosmic rays observed possess macroscopic energies and their origin is likely to be associated with the most energetic…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
A general view is presented on the problem of propagation of ultra high-energy cosmic rays through the intergalactic and galactic magnetic fields. Especial emphasis is given to the possibility of correlating the present events with…
The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…
We consider a problem of finding the maximum attainable energy at a cyclotron as an exercise in the introductory relativity course and comment on some subtle points of the solution.