Quantum Systems with jump-discontinuous mass. I
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910161094836224 |
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| author | Cunden, Fabio Deelan Gramegna, Giovanni Ligabò, Marilena |
| author_facet | Cunden, Fabio Deelan Gramegna, Giovanni Ligabò, Marilena |
| contents | We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by the boundary conditions at the points of mass discontinuity. For a family of scale-free boundary conditions, we analyse the associated spectral problem. We find that the eigenfunctions exhibit a highly sensitive and erratic dependence on the energy. Notably, the system supports infinitely many distinct semiclassical limits, each labeled by a point on a spectral curve embedded in the two-torus. These results demonstrate a rich interplay between discontinuous coefficients, boundary data, and spectral asymptotics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Systems with jump-discontinuous mass. I Cunden, Fabio Deelan Gramegna, Giovanni Ligabò, Marilena Mathematical Physics Spectral Theory Chaotic Dynamics Quantum Physics 81-xx, 34L20, 81Q10 We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by the boundary conditions at the points of mass discontinuity. For a family of scale-free boundary conditions, we analyse the associated spectral problem. We find that the eigenfunctions exhibit a highly sensitive and erratic dependence on the energy. Notably, the system supports infinitely many distinct semiclassical limits, each labeled by a point on a spectral curve embedded in the two-torus. These results demonstrate a rich interplay between discontinuous coefficients, boundary data, and spectral asymptotics. |
| title | Quantum Systems with jump-discontinuous mass. I |
| topic | Mathematical Physics Spectral Theory Chaotic Dynamics Quantum Physics 81-xx, 34L20, 81Q10 |
| url | https://arxiv.org/abs/2505.16913 |