Related papers: On the Aharonov-Casher formula for different self-…
We use a covariant formalism that is capable of describing the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum…
The formulation of Berry for the Aharonov-Bohm effect is generalized to the relativistic regime. Then, the problem of finding the self-adjoint extensions of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background potential,…
We considered a charged quantum mechanical particle with spin ${1\over 2}$ and gyromagnetic ratio $g\ne 2$ in the field af a magnetic string. Whereas the interaction of the charge with the string is the well kown Aharonov-Bohm effect and…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
We investigate the spectrum of the two-dimensional Pauli operator, describing a spin-$1/2$ particle in a magnetic field $B$, with a negative scalar potential $V$ such that $|V|$ grows at infinity. In particular, we obtain criteria for…
We consider the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov--Bohm solenoid field and a collinear uniform magnetic field). Using von Neumann's theory of the self-adjoint extensions of symmetric operators,…
We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schr\"odinger operator, in a quasi-convex domain~$\Omega$ with compact boundary, and magnetic potentials with components in…
Bound states of massive fermions in the Aharonov-Bohm like fields have analytically been studied. The Hamiltonians with the Aharonov--Bohm like potentials are essentially singular and therefore require specification of a one-parameter…
By the Aharonov-Casher theorem, the Pauli operator $P$ has no zero eigenvalue when the normalized magnetic flux $\alpha$ satisfies $|\alpha|<1$, but it does have a zero energy resonance. We prove that in this case a Lieb-Thirring inequality…
We consider a spin-1/2 charged particle in the plane under the influence of two idealized Aharonov-Bohm fluxes. We show that the Pauli operator as a differential operator is defined by appropriate boundary conditions at the two vortices.…
The scattering of electrons by an Aharonov--Bohm field is considered from the viewpoint of quantum-mechanical problem of constructing a self-adjoint Hamiltonian for the Pauli equation. The correct domain for the self-adjoint Hamiltonian,…
In this work, we investigate how both rotation and a Coulomb potential affect the quantum mechanical description of a spin-$1/2$ particle in the presence of the Aharonov-Bohm effect. We employ the method of the self-adjoint extensions in…
In this note, we care to study the degeneracy of the zero modes for a spin-$1/2$ charged particle in a one-dimensional space. We analyze the arguments proposed by Aharonov and Casher in a two-dimensional space. In two dimensions the zero…
The Aharonov-Casher (AC) effect for quantum motion of a neutral magnetized particle in the electric field is believed to be a topological effect closely related to the known Aharonov-Bohm (AB) effect. We study how it depends on the spin of…
We study the two-body Dirac operator in a bounded external field and for a class of unbounded pair-interaction potentials, both repulsive and attractive, including the Coulomb type. Provided the coupling constant of the pair-interaction…
We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p\loc(\R^d)$, and with magnetic potentials in ${L^{q}\loc(\R^d)}$, where ${p >…
We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von…
We establish systematic consolidation of the Aharonov-Bohm and Aharonov-Casher effects including their scalar counterparts. Their formal correspondences in acquiring topological phases are revealed on the basis of the gauge symmetry in…
The method of self-adjoint extensions is employed to determine the vacuum quantum numbers induced by a singular static magnetic vortex in $2+1$-dimensional spinor electrodynamics. The results obtained are gauge-invariant and, for certain…
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point spectrum. The settings…