Related papers: Which magnetic fields support a zero mode?
We consider a Schr\"odinger operator $(h\mathbf D -\mathbf A)^2$ with a positive magnetic field $B=\curl\mathbf A$ in a domain $\Omega\subset\R^2$. The imposing of Neumann boundary conditions leads to spectrum below $h\inf B$. This is a…
We investigate the existence of ground states for the focusing Nonlinear Schr\"odinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass…
We study the influence of a perpendicular magnetic field with the asymptotics $B(r\to \infty)= B_0$ in a electrons in graphene. It is shown that the zero-energy solutions can exist only for one pseudospin direction, depending on the sign of…
Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
In this paper we discuss once more the zero mode contribution to the vacuum energy density. We show that a careful treatment of the zero modes leads to the conclusion that domain walls may be ferromagnetic, and could generate a magnetic…
In this work we investigate the quantum dynamics of an electric dipole in a $(2+1)$-dimensional conical spacetime. For specific conditions, the Schr\"odinger equation is solved and bound states are found with the energy spectrum and…
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schr{\"o}dinger operator involving an Aharonov-Bohm magnetic vector potential. We investigate the symmetry properties of the optimal…
We calculate the energies of various multiple-spiral spin configurations for the three-dimensional model of chiral magnets. The ground-state phase diagram is obtained in the space of anisotropy, magnetic field, and interaction parameters.…
Semiconductor nanowires with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana…
We show that the topological Majorana modes in nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these…
We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that,…
We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…
We investigate the resonant motion of neutral spin-1/2-fermions in a magnetic guide. A wealth of unitary and anti-unitary symmetries is revealed in particular giving rise to a two-fold degeneracy of the energy levels. To compute the…
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…
The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor…