标题： 谱渐近性对于由无限曲线支持的$δ'$相互作用 显示英文标题

标题： Spectral asymptotics for $δ'$ interaction supported by a infinite curve

摘要： 我们考虑在$L^2(\mathbb R^2)$中的广义薛定谔算子，它描述了一个在强耦合极限下的吸引性$\delta'$相互作用。$\delta'$相互作用由一个耦合参数$\beta$表征，并且它由一个$C^4$-光滑的无限渐近直线曲线$\Gamma$支持，该曲线没有自相交。 在强耦合极限下，$\beta\to 0_+$的非直线曲线的本征值行为如$-\frac{4}{\beta^2} +\mu_j+\mathcal O(\beta|\ln\beta|)$所示，其中$\mu_j$是在$L^2(\mathbb R)$上带有势$-\frac14 \gamma^2$的薛定谔算子的第$j$个本征值，其中$\gamma$是$\Gamma$的有符号曲率。 显示英文摘要

摘要： We consider a generalized Schr\"odinger operator in $L^2(\mathbb R^2)$ describing an attractive $\delta'$ interaction in a strong coupling limit. $\delta'$ interaction is characterized by a coupling parameter $\beta$ and it is supported by a $C^4$-smooth infinite asymptotically straight curve $\Gamma$ without self-intersections. It is shown that in the strong coupling limit, $\beta\to 0_+$, the eigenvalues for a non-straight curve behave as $-\frac{4}{\beta^2} +\mu_j+\mathcal O(\beta|\ln\beta|)$, where $\mu_j$ is the $j$-th eigenvalue of the Schr\"odinger operator on $L^2(\mathbb R)$ with the potential $-\frac14 \gamma^2$ where $\gamma$ is the signed curvature of $\Gamma$.