论文标题
磁场对局部变形电线的离散光谱的影响
Magnetic field influence on the discrete spectrum of locally deformed leaky wires
论文作者
论文摘要
我们考虑磁性schrödingeroperator $ h =（i \ nabla +a）^2-αδ_γ$，具有吸引人的单数相互作用，由分段平滑曲线$γ$支持，是直线的局部变形。磁场$ b $应该是非零和本地的。我们表明，基本频谱为$ [ - \frac14α^2，\ infty）$，对于具有笔直$γ$的非磁性运算符，并且证明了$ h $的离散频谱的足够条件，可以为空。
We consider magnetic Schrödinger operator $H=(i \nabla +A)^2-αδ_Γ$ with an attractive singular interaction supported by a piecewise smooth curve $Γ$ being a local deformation of a straight line. The magnetic field $B$ is supposed to be nonzero and local. We show that the essential spectrum is $[-\frac14α^2,\infty)$, as for the non-magnetic operator with a straight $Γ$, and demonstrate a sufficient condition for the discrete spectrum of $H$ to be empty.
