Related papers: Asymptotics for Erdos-Solovej Zero Modes in Strong…
Let $\mathcal{P}_{\Omega,tA}$ denoted the Pauli operator on a bounded open region $\Omega\subset\mathbb{R}^2$ with Dirichlet boundary conditions and magnetic potential $A$ scaled by some $t>0$. Assume that the corresponding magnetic field…
In this paper, we consider the 2D- Schr\"odinger operator with constant magnetic field $H(V)=(D_x-By)^2+D_y^2+V_h(x,y)$, where $V$ tends to zero at infinity and $h$ is a small positive parameter. We will be concerned with two cases: the…
Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $ D=\frac{1}{i} \nabla_x$, and…
We investigate the two-dimensional magnetic operator $H_{c_0,B,\beta} = {(-i\nabla -A)}^{2}-\beta\delta(.-\Gamma),$ where $\Gamma$ is a smooth loop. The vector potential has the form $A=c_0\bigg(\frac{-y}{{x^2+y^2}}; \frac{x}{{x^2+y^2}}…
In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in $\mathbb{S}^3$ (and $\mathbb{R}^3$) by Dirac operators with smooth magnetic fields. We then proceed to prove that under certain…
We consider magnetic fields on $\mathbb{R}^3$ which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic field cannot have a zero mode. In particular…
We show that magnetic zero-modes of the Dirac operator on $\mathbb{R}^3$ which obey an additional non-linear equation are closely related to vortex configurations on the 2-sphere, and that both are best understood in terms of the geometry…
This paper presents some results concerning the size of magnetic fields that support zero modes for the three dimensional Dirac equation and related problems for spinor equations. It is a well known fact that for the Schr\"odinger in three…
We consider the Pauli operator in $\mathbb R^3$ for magnetic fields in $L^{3/2}$ that decay at infinity as $|x|^{-2-\beta}$ with $\beta > 0$. In this case we are able to prove that the existence of a zero mode for this operator is…
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…
We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be interpreted in a simple manner in terms of a stereographic projection from a 4d Dirac operator with a constant field strength of definite helicity. This is an…
We study the asymptotic behavior, as Planck's constant $\hbar\to 0$, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field $\mu\mathbf{B}(x)$ and an electric field. The magnetic field…
Sharp spectral asymptotics for 2- and 3-dimensional Schroedinger operators with strong magnetic field are derived under rather weak smoothness conditions. In comparison with version 1 of 2005 new results are added and minor errors…
We consider a 3-dimensional Dirac operator H_0 with non-constant magnetic field of constant direction, perturbed by a sign-definite matrix-valued potential V decaying fast enough at infinity. Then we determine asymptotics, as the energy…
We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit…
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we…
The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein-Yang-Mills background fields with a half-integer Chern-Simons number. The proof holds for any gauge group and applies to Dirac…
The study of interplay between the geometric nature of Bloch electrons and transverse responses under strong field offers new opportunities for optoelectronic applications. Here, we present a comprehensive study of the strong-field response…
We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function.…
We investigate the two-dimensional Aharonov-Bohm operator $H_{c_0,\beta} = {(-i\nabla -A)}^{2}-\beta\delta(.-\Gamma),$ where $\Gamma$ is a smooth loop and $A$ is the vector potential which corresponds to Aharonov-Bohm potential. The…