1997/10/01 by T. Shigehara, Takaomi Shigehara, Hiroshi Mizoguchi +8
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Chaotic Dynamics (nlin.CD) #Condensed Matter (cond-mat) #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories #chao-dyn #cond-mat #nlin.CD #nucl-th #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9710005
Manuscript for Proceedings of The 8th International Colloquium on Differential Equations Plovdiv, Bulgaria, 18-23 August, 1997
arxiv created 1997/10/01 · openalex publication_date 1997/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss spectral properties of the Laplacian with multiple (N) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a symmetric (Hermitian) operator in functional analysis. The eigenvalues of this system are obtained as the poles of a transition matrix which has size N. Closely examining a generic behavior of the eigenvalues of the transition matrix as a function of the energy, we deduce the general condition under which point interactions have a substantial effect on statistical properties of the spectrum.