Related papers: Singular spin-flip interactions for the 1D Schr\"{…
We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at…
All relativistic corrections to the Scr{\"o}dinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among…
In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially…
We show that dynamics in spin-orbit coupling field simulates the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a…
We show that the operators and the quadrupole and Zeeman Hamiltonians for a spin (3/2) can be represented in terms for a system of two coupling fictitious spins (1/2) using the Kronecker product of Pauli matrices. Particularly, the…
We study the Schr\"{o}dinger operator describing a two-dimensional quantum particle moving in presence of $ N \geqslant 1 $ Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an…
We show that formal Schr\"odinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the…
Spin-flips are one of the limiting factors for spin-based information processing. We demonstrate a transport approach for determining the spin-flip rates of a self-assembled InAs double quantum dot occupied by a single electron. In such…
We analytically evaluate charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies. On the basis of our exact expressions we discuss the accuracy…
The influence of spin-orbit coupling in two-dimensional systems is investigated within the framework of the Landauer-Buettiker coherent scattering formalism. This formalism usually deals with spin-independent stationary states and,…
We provide a full characterization of the spectral properties of spiral spin density wave (SSDW) states which emerge in one-dimensional electron systems coupled to localized magnetic moments or quantum wires with spin-orbit interactions. We…
In the present paper our aim is to explore some spectral properties of the family two-particle discrete Schr\"odinger operators $h^{\mathrm{d}}(k)=h^{\mathrm{d}}_0(k)+ \mathbf{v},$ $k\in \T^\mathrm{d},$ on the $\mathrm{d}$ dimensional…
In this paper we consider the two-dimensional Schr\"odinger operator with an attractive potential which is a multiple of the characteristic function of an unbounded strip-shaped region, whose thickness is varying and is determined by the…
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a…
Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $\delta$ and $\delta '$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by…
This paper summarizes the contents of a plenary talk at the Pan African Congress of Mathematics held in Rabat in July 2017. We provide a survey of recent results on spectral properties of Schr\"odinger operators with singular interactions…
We develop a theory of designing slit experiments in two-dimensional electron systems with the Rashba spin-orbit interaction. By simulating the spatiotemporal dynamics of electrons passing through a single slit or a double slit, we find…
Spin-charge separation is known to be broken in many physically interesting one-dimensional (1D) and quasi-1D systems with spin-orbit interaction because of which spin and charge degrees of freedom are mixed in collective excitations. Mixed…
We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the \delta-function singularity coming from the…
This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of…