Spectrum of the Dirac operator in shrinking tubes

Nour Kerraoui (1)

1 I2M - Institut de Mathématiques de Marseille

In this paper we investigate the spectrum of the Dirac operator posed in a tubular neighborhood of a planar loop with infinite mass boundary conditions. We show that when the width of the tubular neighborhood goes to zero the asymptotic expansion of the eigenvalues is driven by a one dimensional operator of geometric nature involving the curvature of the loop.

Mots clés: Spectral theory; asymptotic analysis; Dirac operator

Domaines: Théorie spectrale [math.SP]

Nour Kerraoui. Spectrum of the Dirac operator in shrinking tubes. 2023. ⟨hal-04021175⟩