Related papers: Magnetic flatness and E. Hopf's theorem for magnet…
We focus on quantum systems that can be effectively described as a localized spin-$s$ particle subject to a static magnetic field coplanar to a coexisting elliptically rotating time-periodic field. Depending on the values taken on by the…
It is known that a system which exhibits a half filled lowest flat band and the localized one-particle Wannier states on the flat band satisfy the connectivity conditions, is always ferromagnetic. Without the connectivity conditions on the…
Magnetic nulls are locations where the magnetic field vanishes. Nulls are the location of magnetic reconnection, and they determine to a large degree the magnetic connectivity in a system. We describe a novel approach to understanding…
It is well-known that a minimal graph of codimension one is stable, i.e. the second variation of the area functional is non-negative. This is no longer true for higher codimensional minimal graphs. In this note, we prove that a minimal…
Let $H^p(L^2(M))$ be the space of all $L^2$-harmonic $p$-forms $(2\leq p\leq n-2)$ on complete submanifolds $M$ with flat normal bundle in spheres. In this paper, we first show that $H^p(L^2(M))$ is trivial if the total curvature of $M$ is…
We study charged-fluid toroidal structures surrounding a non-rotating charged black hole immersed in a large-scale, asymptotically uniform magnetic field. In continuation of our former study on electrically charged matter in approximation…
In the framework of the nonlinear stability of Minkowski spacetime, we show that if the radiation field of the curvature tensor vanishes, the spacetime must be flat.
A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…
Most studies of the pulsar magnetosphere have assumed a pure magnetic dipole in flat spacetime. However, recent work suggests that the effects of general relativity are in fact of vital importance and that realistic pulsar magnetic fields…
We consider the stability of a configuration consisting of a vertical magnetic field in a planar flow on elliptical streamlines in ideal hydromagnetics. In the absence of a magnetic field the elliptical flow is universally unstable (the…
In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the…
We shall construct a natural Higgs bundle structure on the complexified K\"ahler cone of a compact K\"ahler manifold, which can be seen as an analogy of the classical Higgs bundle structure associated to a variation of Hodge structure. In…
In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this…
We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines changes under the flow. By Alfv\'en's theorem this is known to be…
We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^\alpha, heuristically, the generator of time-translations in a corotating frame. Systems that are…
The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas and the dynamics of Alfv\'en waves are governed by a system of nonlinear partial differential equations called the MHD system. In this paper, we study the rigidity…
We prove the following generalization of the classical Lichnerowicz vanishing theorem: if $F$ is an oriented flat vector bundle over a closed spin manifold $M$ such that $TM$ carries a metric of positive scalar curvature, then $<\widehat…
We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection…
We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge…
Let M be a compact complex surface which admits a Kaehler metric whose scalar curvature has integral zero; and suppose the fundamental group of M does not contain an Abelian subgroup of finite index. Then if M is blown up at sufficiently…