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arXiv · 2505.17920

Isospectrality and non-locality of generalized Dirac combs

Giuliano Angelone·Manuel Asorey·Fernando Ezquerro·Paolo Facchi
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Abstract

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 $\delta$-potential and the $\delta'$-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.

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Giuliano Angelone, Manuel Asorey, Fernando Ezquerro, Paolo Facchi. 2025-05-23. Isospectrality and non-locality of generalized Dirac combs. https://doi.org/10.1088/1751-8121%2Fae0847

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