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arXiv · 2312.16701

Integral formulation of Dirac singular waveguides

Guillaume Bal·Jeremy Hoskins·Solomon Quinn·Manas Rachh
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Abstract

This paper concerns a boundary integral formulation for the two-dimensional massive Dirac equation. The mass term is assumed to jump across a one-dimensional interface, which models a transition between two insulating materials. This jump induces surface waves that propagate outward along the interface but decay exponentially in the transverse direction. After providing a derivation of our integral equation, we prove that it has a unique solution for almost all choices of parameters using holomorphic perturbation theory. We then extend these results to a Dirac equation with two interfaces. Finally, we implement a fast numerical method for solving our boundary integral equations and present several numerical examples of solutions and scattering effects.

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Guillaume Bal, Jeremy Hoskins, Solomon Quinn, Manas Rachh. 2023-12-27. Integral formulation of Dirac singular waveguides. https://doi.org/10.2140/paa.2026.8.331

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