Spectral gap of generalized MIT bag models

Authors

  • Joaquim Duran i Lamiel

Keywords:

Dirac operator, spectral theory, MIT bag model, shape optimization, resolvent convergence.

Abstract

Estudiem propietats espectrals dels models de bossa de l’MIT generalitzats. Aquests són operadors de Dirac {Hτ }τ∈R actuant en dominis de R3 amb condicions de frontera que generen confinament. El seu autovalor positiu més baix és d’especial interès, i s’ha conjecturat que és mínim per a una bola entre tots els dominis amb volum fixat. La conjectura anàloga és certa per al laplacià de Dirichlet (és la desigualtat de Faber–Krahn), que sorgeix en els límits τ → ±∞. Estudiant la convergència en el sentit de la resolvent dels operadors Hτ; cap als operadors límit H±∞; quan τ → ±∞, provem que certes propietats espectrals s’hereden al llarg de la parametrització. Aquests resultats són nous i s’han publicat a [3].

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How to Cite

Duran i Lamiel, J. (2024). Spectral gap of generalized MIT bag models. Reports@SCM, 9(1), 95–96. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154347

Issue

Vol. 9 No. 1 (2024)

Section

Extended abstracts

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