Hearing the boundary conditions of the one-dimensional Dirac operator

Giuliano Angelone

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arXiv · 2311.17561

Hearing the boundary conditions of the one-dimensional Dirac operator

Giuliano Angelone

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Abstract

We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of the boundary conditions at the junction, characterizing the energy spectrum by means of a spectral function. By determining the symmetries of the latter, we are able to divide the self-adjoint extensions in two classes, identifying all the families of isospectral Hamiltonians, and thus completely characterizing the isospectrality problem.

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Giuliano Angelone. 2023-11-29. Hearing the boundary conditions of the one-dimensional Dirac operator. https://arxiv.org/abs/2311.17561

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