Isospectrality and non-locality of generalized Dirac combs

Angelone, Giuliano ; Asorey, Manuel (Universidad de Zaragoza) ; Ezquerro, Fernando (Universidad de Zaragoza) ; Facchi, Paolo

Resumen: We consider a generalization of Dirac’s comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy operator self-adjoint, and form a four-parameters family that includes the δ-potential and the δ-potential as particular cases. We study the parameter dependence of the spectral properties of this system, finding a rich isospectrality structure. We systematically classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation.

Idioma: Inglés

DOI: 10.1088/1751-8121/ae0847

Año: 2025

Publicado en: Journal of Physics A-Mathematical and Theoretical 58, 39 (2025), 395301 [33 pp.]
ISSN: 1751-8113

Tipo y forma: Article (Published version)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)