相关论文: The Stationary Maxwell-Dirac Equations
In this paper we formulate Maxwell and Dirac theories as an already unified theory (in the sense of Misner and Wheeler). We introduce Dirac spinors as "Dirac square root" of the Faraday bivector, and use this in order to find a spinorial…
We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…
We investigate dispersive estimates for the massless three dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $\langle t\rangle^{-1}$ decay rate as an operator from $L^1$ to $L^\infty$…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
In this work we study the electric field of a dipole immersed in a medium with permittivity controlled by a real scalar field which is non-minimally coupled to the Maxwell field. We model the system with an interesting function, which…
We analyse how the spectrum of the anisotropic Maxwell system with bounded conductivity on a Lipschitz domain is approximated by domain truncation. First we prove a new non-convex enclosure for the spectrum of the Maxwell system, with weak…
The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
We establish local energy decay for damped magnetic wave equations on stationary, asymptotically flat space-times subject to the geometric control condition. More specifically, we allow for the addition of time-independent magnetic and…
The nature of spin current and the separation of charge current and spin current are two of the fundamental questions in spintronics. For this purpose the classical limit of the Maxwell-Dirac theory is investigated in the present…
The energy of solutions of the scalar damped wave equation decays uniformly exponentially fast when the geometric control condition is satisfied. A theorem of Lebeau [leb93] gives an expression of this exponential decay rate in terms of the…
We consider the stabilization problem on a manifold with boundary for a wave equation with measure-valued linear damping. For a wide class of measures, containing Dirac masses on hypersurfaces as well as measures with fractal support, we…
The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A…
In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter…
From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity the uniqueness of wide families of exact solutions is established, among them, all…
The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is…
We construct Einstein-Maxwell-Scalar (EMS) theories that admit regular electric black holes. Such a Maxwell-scalar theory is equivalent to some nonlinear electrodynamics (NLED) at the level of equations of motion, but it has the advantage…
Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This…