On the asymptotic number of low-lying states in the two-dimensional confined Stark effect

2024/04/22 by Read, Larry · 1 citation
#35P20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2404.14363

Abstract

We investigate the Stark operator restricted to a bounded domain Ω⊂ℝ² with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been established, with coefficients dependent on the curvature of Ω. We analyse the accumulation of eigenvalues beneath the leading-order terms in these expansions, establishing Weyl-type asymptotics. Furthermore, we derive weak asymptotics for the density of the spectral projector onto these low-lying states.

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