Related papers: Visualizing the kinematics of relativistic wave pa…
Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations. Dynamics of the group velocity of a massless particle as a whole and of the corresponding radius vector is determined. This radius vector…
This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in $R^{1+1}$. It is shown that the solution will tend to travelling wave solution when time tends to infinity.
Exact analytic solutions of the time dependent Schrodinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are…
Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their…
We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the…
The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible…
We investigate the propagation of a wave--packet in the $\phi^4$ model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink…
This paper shows as the relativistic Doppler effect can be extended also to time and space associated to moving bodies. This extension derives from the analysis of the wave-fronts of the light emitted by a moving source in inertial motion…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
We use the conservation law of the stress-energy and spin tensors to study the motion of massive zero-size objects in Riemann-Cartan geometry. The resultant world line equations turn out to exhibit a novel spin-curvature coupling. In…
We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point source initial condition. We show that in both the propagation, and Klein-tunneling regimes, the…
Radiative transfer equation in an accretion disk wind is examined analytically and numerically under the plane-parallel approximation in the subrelativistic regime of $(v/c)^1$, where $v$ is the wind vertical velocity. Emergent intensity is…
A basic problem in the relativistic quantum Hamilton-Jacobi theory is to understand whether it may admit superluminal solutions. Here we consider the averaging of the speed on a period of the oscillating term which is similar to Dirac's…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…
The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total…
The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein…
A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ -- D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free…
Zitterbewegung is a striking consequence of relativistic quantum mechanics which predicts that free Dirac electrons exhibit a rapid trembling motion even in the absence of external forces. The trembling motion of an electron results from…
In a recent paper [1], it has been proposed that relativistic wave-particle duality can be embodied in a relation that shows that the four-velocity of a particle is proportional to the Dirac four-current. In this note we bring out some…
We consider electronic transport accross one-dimensional heterostructures described by the Dirac equation. We discuss the cases where both the velocity and the mass are position dependent. We show how to generalize the Dirac Hamiltonian in…