Sharp exponential localization for eigenfunctions of the Dirac Operator

We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and $\mathbb V$ a matrix-valued perturbation such that $|\mathbb V(x)| \sim |x|^{-\epsil...

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Detalles Bibliográficos
Autor: Cassano, B.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/813
Acceso en línea:http://hdl.handle.net/20.500.11824/813
Access Level:acceso abierto
Palabra clave:Dirac operator, unique continuation, complex potentials, localization of eigenfunctions
Descripción
Sumario:We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and $\mathbb V$ a matrix-valued perturbation such that $|\mathbb V(x)| \sim |x|^{-\epsilon}$ at infinity, for $\epsilon < 1$. Moreover, we provide explicit examples of solutions that have the prescripted decay, in presence of a potential with the related behaviour at infinity, proving that our results are sharp. This work is a result of unique continuation from infinity.

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