A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities

DOI10.1007/s00220-021-03959-6zbMath1472.81090arXiv2003.04061OpenAlexW3164904278MaRDI QIDQ2046788

Thomas Ourmières-Bonafos, Rafael D. Benguria, Vladimir Lotoreichik, Pedro R. S. Antunes

Publication date: 19 August 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04061

zbMATH Keywords

variational formulationprincipal eigenvalueFaber-Krahn type inequalityinfinite mass boundary conditionsDirac Operators

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Spinor and twistor methods applied to problems in quantum theory (81R25) Hardy spaces (30H10) Bergman spaces and Fock spaces (30H20)

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Spectral optimization of Dirac rectangles ⋮ Spectral inequality for Dirac right triangles ⋮ The Dirac bag model in strong magnetic fields ⋮ Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation ⋮ Eigenvalue curves for generalized MIT bag models ⋮ A Dirac-fermions functional for Coulomb interaction on arbitrary (fractional) dimension: energy and pressure ⋮ Faber–Krahn inequalities for Schrödinger operators with point and with Coulomb interactions ⋮ Dirac operator spectrum in tubes and layers with a zigzag-type boundary

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