Dispersive decay estimates for Dirac equations with a domain wall
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914875561738240 |
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| author | Kraisler, Joseph Sagiv, Amir Weinstein, Michael I. |
| author_facet | Kraisler, Joseph Sagiv, Amir Weinstein, Michael I. |
| contents | Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and $x=-\infty$. This family of Hamiltonians arises in the theory of topologically protected states of one-dimensional quantum materials. For certain values of the phase-shift parameter, $τ$, the Dirac Hamiltonian has a {\it threshold resonance} at the endpoint of its essential spectrum. Such resonances are known to influence the time-decay rate. Our main result explicitly displays the transition in time-decay rate as $τ$ varies between resonant and non-resonant values. Our results appear to be the first dispersive time-decay estimates for Dirac Hamiltonians which are not a relatively compact perturbation of a free Dirac operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dispersive decay estimates for Dirac equations with a domain wall Kraisler, Joseph Sagiv, Amir Weinstein, Michael I. Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and $x=-\infty$. This family of Hamiltonians arises in the theory of topologically protected states of one-dimensional quantum materials. For certain values of the phase-shift parameter, $τ$, the Dirac Hamiltonian has a {\it threshold resonance} at the endpoint of its essential spectrum. Such resonances are known to influence the time-decay rate. Our main result explicitly displays the transition in time-decay rate as $τ$ varies between resonant and non-resonant values. Our results appear to be the first dispersive time-decay estimates for Dirac Hamiltonians which are not a relatively compact perturbation of a free Dirac operator. |
| title | Dispersive decay estimates for Dirac equations with a domain wall |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2307.06499 |