具有$δ$ -和$δ'$ -柱相互作用的Landau算子的相对论谱性质
Relativistic Spectral Properties of Landau Operator with $δ$- and $δ'$- cylinder interactions
摘要：
利用自伴延拓理论，研究了带电自旋粒子系统中具有$δ$和$δ'$相互作用的Landau算符在半径为$R$的圆柱体上的相对论谱性质，形式为作用在$ L^2(\R^2)\bigotimes \C^2 $中的哈密顿量$H^G_{B} = {(p-A)}^2 I + {\bfσ}.{\bf{B}+G}V(r),$ $\bigg(V(r) = δ(R-r)$或$V(r) = δ' (R-r) \bigg),$. $G$是标量$2\times 2$实矩阵。I是单位矩阵。势矢量具有$A= (B/2)(-y, x)$和$B>0.$的形式
英文摘要：
Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $δ$ and $δ'$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by the Hamiltonian $H^G_{B} = {(p-A)}^2 I + {\bfσ}.{\bf{B}+G}V(r),$ $\bigg(V(r) = δ(R-r)$ or $V(r) = δ' (R-r) \bigg),$ 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 $B>0.$
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