2015/07/02 by Andreas Fring
Mathematics · Physics and Astronomy · #Biorthogonal system #Eigenvalues and eigenvectors #Limit (mathematics) #Mathematical functions and polynomials #Measure (data warehouse) #Orthogonal polynomials #Quantum Mechanics and Non-Hermitian Physics #Scaling #Scaling limit #Space (punctuation) #Spectral Theory in Mathematical Physics #Type (biology) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/978-3-319-31356-6_15
14 pages, 5 figures, prepared for Selected Contributions in Springer Proceedings in Physics
arxiv created 2015/07/02 · openalex publication_date 2016/01/01 · arxiv updated 2016/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A new non-Hermitian E2-quasi-exactly solvable model is constructed containing two previously known models of this type as limits in one of its three parameters. We identify the optimal finite approximation to the double scaling limit to the complex Mathieu Hamiltonian. A detailed analysis of the vicinity of the exceptional points in the parameter space is provided by discussing the branch cut structures responsible for the chirality when exceptional points are surrounded and the structure of the corresponding energy eigenvalue loops stretching over several Riemann sheets. We compute the Stieltjes measure and momentum functionals for the coefficient functions that are univariate weakly orthogonal polynomials in the energy obeying three-term recurrence relations.