Related papers: Zero modes for the magnetic Pauli operator in even…
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…
We find a class of Fermion zero modes of Abelian Dirac operators in three dimensional Euclidean space where the gauge potentials and the related magnetic fields are nonzero only in a finite space region.
We establish that the Pauli operator describing a spin-1/2 two-dimensional quantum system with a singular magnetic field has, under certain conditions, an infinite-dimensional space of zero modes, possibly, both spin-up and spin-down,…
We consider the three-dimensional Laplacian with a magnetic field created by an infinite rectilinear current bearing a constant current. The spectrum of the associated hamiltonian is the positive half-axis as the range of an infinity of…
We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli…
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…
We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kova\v{r}\'ik-Portmann and Helffer-Sundqvist for the asymptotics of…
We consider eigenvalues of the Pauli operator in $\mathbb R^3$ embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and…
In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in noncommutative phase-space, as well the corresponding deformed continuity equation, where the cases of a…
We consider a polygon in a two-dimensional plane with a homogeneous constant magnetic field orthogonal to such plane, but inside the polygon, the magnetic field is zero. We study the dynamics of an electron with an initial velocity in this…
The half-filled two-dimensional Hubbard model in presence of a uniform and static parallel magnetic field has been studied by means of the Composite Operator Method. A fully self-consistent solution, fulfilling all the constrains coming…
Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\rm…
In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we derive wave function and energy spectrum of a spin half non-relativistic charged particle that is moving under a constant magnetic field with…
We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not vanish identically, then the classical lower…
We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.
We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of…
In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field…
We consider a 2D Pauli operator with almost periodic field $b$ and electric potential $V$. First, we study the ergodic properties of $H$ and show, in particular, that its discrete spectrum is empty if there exists an almost periodic…
Two results are proved for $\mathrm{nul} \mathbb{P}_A$, the dimension of the kernel of the Pauli operator $\mathbb{P}_A = \bigl\{\bbf{\sigma} \cdotp \bigl(\frac{1}{i} \bbf{\nabla} + \vec{A} \bigr) \bigr\} ^2 $ in $[L^2 (\mathbb{R}^3)]^2$:…
We consider the large-$U$ limit of the one-band Hubbard model at half-filling on a non-bipartite two-dimensional lattice. An external magnetic field can induce a three-spin chiral interaction at order $1 / U^2 ~$. We discuss situations in…