Relativistic Spectral Properties of Landau Operator with $\delta$- and ${\delta }^{\prime }$- cylinder interactions

Abstract

Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $\delta$ and ${\delta }^{\prime }$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by the Hamiltonian $H_B^G={(p-A)}^{2}I+\sigma .\mathbf{B}+\mathbf{G}V(r),$ $(V(r)=\delta (R-r)$ or $V(r)={\delta }^{\prime }(R-r)),$ acting in $ L^2(\R^2)\bigotimes \C^2 $. $G$ a scalar $2\times 2$ real matrix. I is the identity matrix. The potential vector has the form $A=(B/2)(-y,x)$ and $B>0.$

16 pages