2025/12/12 by Li, Shimei, Zhang, Kai, Zhao, Jia
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2512.11227
openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28
We consider a Cartesian product quantum graph Γn1\BoxΓn2 with standard vertex conditions, and complete the decomposition of Hilbert space L2(Γn1\BoxΓn2) and the Laplacian \mathscrH on it by employing the relevant theories of group representation. The concept of Γn1\BoxΓn2 equipped with the action of the cyclic group Gn1× Gn2 is defined through the introduction of periodic quantum graph and cyclic groups. We also constructed its quotient graph and accomplish the decomposition of its secular determinant. Furthermore, under the condition that gcd(n1,n2)=1, it can be regarded as equivalent to a circulant graph Cn1n2(n1,n2). This work also provides a new method for the construction of isospectral graphs.