Spectral optimisation of Dirac rectangles - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2022

Spectral optimisation of Dirac rectangles

Résumé

We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the area or perimeter constraints. Contrary to well-known non-relativistic analogues, we show that the present spectral problem does not admit explicit solutions. We prove partial optimisation results based on a variational reformulation and newly established lower and upper bounds to the Dirac eigenvalue. We also propose an alternative approach based on symmetries of rectangles and a non-convex minimisation problem; this implies a sufficient condition formulated in terms of a symmetry of the minimiser which guarantees the conjectured results.

Dates et versions

hal-03491686 , version 1 (17-12-2021)

Identifiants

Citer

Philippe Briet, David Krejcirik. Spectral optimisation of Dirac rectangles. Journal of Mathematical Physics, 2022, 63 (1), pp.013502. ⟨10.1063/5.0056278⟩. ⟨hal-03491686⟩
30 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More