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arXiv · 2307.06499

Dispersive decay estimates for Dirac equations with a domain wall

Joseph Kraisler·Amir Sagiv·Michael I. Weinstein
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Abstract

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.

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Joseph Kraisler, Amir Sagiv, Michael I. Weinstein. 2024-07-18. Dispersive decay estimates for Dirac equations with a domain wall. https://arxiv.org/abs/2307.06499

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