论文标题
有效的量子哈密顿量在具有非均匀性的薄域中
Effective quantum Hamiltonian in thin domains with non-homogeneity
论文作者
论文摘要
我们认为在尼曼边界条件下，在任意维度的欧几里得空间中，在欧几里得空间中的紧凑型超表面的管状邻域中，具有非均匀度量的拉普拉斯人。结果表明，在邻域缩小到零的宽度的极限中，操作员以广义的规范旋转意义收敛到Hypersurface上有效的Laplace-Beltrami-type操作员。通过这种方式，我们概括并深入了解Yachimura（Arxiv：1706.05027）获得的特征值的收敛性。
We consider the Laplacian with a non-homogeneous metric in a tubular neighbourhood of a compact hypersurface in the Euclidean space of arbitrary dimension, subject to Neumann boundary conditions. It is shown that, in the limit of the width of the neighbourhood shrinking to zero, the operator converges in a generalised norm-resolvent sense to an effective Laplace-Beltrami-type operator on the hypersurface. In this way, we generalise and give an insight into the convergence of eigenvalues obtained by Yachimura (arXiv:1706.05027).
