标题： 由可穿透圆壁引起的朗道能级的光谱展宽 显示英文标题

标题： Spectral Broadening of Landau Levels by a Penetrable Circular Wall

摘要： 我们研究了由$\delta$-相互作用建模的可渗透圆形墙的二维磁 Schrödinger 算子。 利用边界三元组方法，我们分类了所有自伴扩张并得到了 Krein 的预解式公式，表明本质谱与 Landau 能级一致。 该墙打破了它们的无限简并性并产生了谱展宽：每个 Landau 能级成为来自一侧的离散本征值的聚点。 在圆形情况下，旋转对称性将本征值问题简化为具有显式 Weyl 系数的标量方程。 我们证明了严格单调性，确保每个角动量通道在每个间隙中最多贡献一个本征值，并推导了渐近行为，表明边界系数衰减快于任何指数，解释了展宽谱的强局域化。 数值模拟与这些结果一致。 显示英文摘要

摘要： We study the two--dimensional magnetic Schr\"odinger operator with a penetrable circular wall modeled by a $\delta$--interaction. Using the boundary triple approach we classify all self--adjoint extensions and obtain Krein's resolvent formula, showing that the essential spectrum coincides with the Landau levels. The wall breaks their infinite degeneracy and produces a spectral broadening: each Landau level becomes an accumulation point of discrete eigenvalues from one side. In the circular case, rotational symmetry reduces the eigenvalue problem to scalar equations with explicit Weyl coefficients. We prove strict monotonicity, ensuring that each angular momentum channel contributes at most one eigenvalue per gap, and derive asymptotics showing that the boundary coefficients decay faster than any exponential, explaining the strong localization of the broadened spectrum. Numerical simulations are consistent with these results.