Related papers: On the Pauli operator for the Aharonov-Bohm effect…
The quantum nonrelativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N=2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two…
The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic 2D Pauli Operator is considered as a by-product of the new reduction found by the present authors few years ago for the Algebrogeometric Inverse Spectral Data…
The Bloch--Torrey operator $-h^2\Delta+e^{i\alpha}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $\alpha\in\left[0,\frac{3\pi}{5}\right)$ and a non-degeneracy assumption on the…
We study deep inelastic scattering (DIS) of charged leptons from polarised spin-1/2 hadrons in terms of the gauge/gravity duality. We calculate the structure functions related to spin-1/2 fermionic operators of ${\cal {N}}=4$ SYM theory in…
The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each consisting…
The Aharonov-Bohm (AB) effect is an important discovery of quantum theory. It serves as a surprising quantum phenomenon in which an electrically charged particle can be affected by an electromagnetic potential, despite being confined to a…
The description of particles with spin can be attained by using a spin density matrix in high energy reaction. In this paper we present a parametrization of the spin density matrix for spin -3/2 particles in the Cartesian form. Comparing…
In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded planar domain. We establish a sharp relation between the rate of…
We present the rigorous derivation of covariant spin operators from a general linear combination of the components of the Pauli-Lubanski vector. It is shown that only two spin operators satisfy the spin algebra and transform properly under…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schr\"odinger operators has no point…
Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure…
We study all the s.a. Schrodinger and Dirac operators (Hamiltonians) both with pure AB field and with magnetic-solenoid field. Then, we perform a complete spectral analysis for these operators, which includes finding spectra and spectral…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
The article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which…
Effective electric and magnetic polarizabilities of pointlike spin-1/2 particles possesing an anomalous magnetic moment are calculated with the transformation of an initial Hamiltonian to the Foldy-Wouthuysen representation.…
The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schr\"{o}dinger equation on a double connected plane. It is a summation over the angular momentum quantum…
For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix is related to one of the generators of rotation in the…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…