Related papers: Stability of Matter in Magnetic Fields
Stability of matter with Coulomb forces has been proved for non-relativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic fields. In both cases stability requires that the fine…
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if $\alpha$ or $Z$ is too large. Here we prove that matter {\it is stable\/} if $\alpha<0.06$ and $Z\alpha^2<0.04$.
We investigate the 50-year old hypothesis that the magnetic fields of the Ap stars are stable equilibria that have survived in these stars since their formation. With numerical simulations we find that stable magnetic field configurations…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…
Magnetic fields represent a crucial aspect of the physics and astrophysics of neutron stars. Despite its great relevance, the internal magnetic field configuration of neutron stars is very poorly constrained by the observations, and…
This paper continues the author's work \cite{PartI}, where a new framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation discovered. Here, the nonlinear Dirac equation is solved and…
The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown that the four-component Dirac equation in arbitrary magnetic…
Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic field configurations were left over after the annihilation of constituents that formed metastable Q=0 configurations. These so-called Dirac sheet…
Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability…
In the paper a new class of exact localized solutions of Dirac's equation in the field of a circularly polarized electromagnetic wave and a constant magnetic field is presented. These solutions possess unusual properties and are applicable…
We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…
It is shown that the electric current of massive fermions along the external magnetic field can be excited in the case when particles possess anomalous magnetic moments and electroweakly interact with background matter. This current is…
We consider the system of massive electrons, possessing nonzero anomalous magnetic moments, which electroweakly interact with background neutrons under the influence of an external magnetic field. The Dirac equation for such electrons is…
We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
The main aim of this work was to give constructive proof of stable orbital motions existence in the systems of bodies, which interact only by magnetic forces.
We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In…
Perturbations of the Dirac field in the Schwarzschild spacetime are characterized by two wave equations (for two chiralities) with effective potentials which are iso-spectral and one of which is positive definite. Therefore, the stability…