ζ-function for a model with spectral dependent boundary conditions
Abstract We explore the meromorphic structure of the ζ -function associated with the boundary eigenvalue problem of a modified Sturm–Liouville operator subject to spectral-dependent boundary conditions at one end of a segment of length l . We find that it presents isolated simple poles that follow the general rule valid for second-order differential operator subject to standard local boundary conditions. We employ our results to evaluate the determinant of the operator and the Casimir energy of the system it describes, and study its dependence on l for both the massive and the massless cases.
Authors
- M. Loewe (ORCID: https://orcid.org/0000-0002-8998-6923)
- Enrique Muñoz (ORCID: https://orcid.org/0000-0003-4457-0817)
- J. C. Rojas (ORCID: https://orcid.org/0000-0002-3888-7538)
- H. Falomir (ORCID: https://orcid.org/0000-0001-8188-1062)
Institutions
- University of Cape Town (ZA)
- Pontificia Universidad Católica de Chile (CL)
- Universidad Católica del Norte (CL)
- San Sebastián University (CL)
- Hospital Luis Calvo Mackenna (CL)
- Instituto de Física La Plata (AR)
Publication Details
- Journal
- Journal of Physics A Mathematical and Theoretical
- Published
- 2025-02-07
- DOI
- https://doi.org/10.1088/1751-8121/adb403
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Universidad Nacional de La Plata
- Fondo Nacional de Desarrollo Científico y Tecnológico