Related papers: The global dynamics for the Maxwell-Dirac system
In this paper, we investigate the characteristic initial value problem for the Einstein-Dirac system, a model governing the interaction between gravity and spin-$1/2$ fields. We apply Luk's strategy \cite{Luk12} and prove a semi-global…
The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case…
This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the assumptions that the initial data has small charge and is…
In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
We study in the framework of relativistic quantum mechanics the evolution of a system of two Dirac neutrinos that mix with each other and have non-vanishing magnetic moments. The dynamics of this system in an external magnetic field is…
Dirac's formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities…
The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and…
In this article, we consider the infinite dimensional vector-valued resonant nonlinear Schr\"odinger system, which arises from the study of the asymptotic behavior of the defocusing nonlinear Schr\"{o}dinger equation on "wave guide"…
We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of…
This paper is concerned with the long time dynamics of the free boundary of a Darcy fluid in three space dimensions, also known as the one-phase Muskat problem. The dynamics of the free boundary is governed by a nonlocal fully nonlinear…
Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed in the framework of the theory of evolutionary equations.…
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner…
A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron-electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the…
In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary…
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined…
The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission…
We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
We consider Einstein-Maxwell-Dilaton (EMD) Lagrangian supplemented by double Liouville potentials to enrich our system and investigate the resulting dynamics. The general solution provides us alternative structures induced on the…