Eigenvalue Asymptotics Near a Flat Band in the Presence of a Slowly Decaying Potential
Year: 2025
Type: article
Abstract: We provide eigenvalue asymptotics for a Dirac-type operator on Z n , n ⩾ 2 , perturbed by multiplication operators that decay as | μ | − γ with γ < n . We show that the eigenvalues accumulate near the value of the flat band at a “semiclassical” rate with a constant that encodes the structure of the flat band. Similarly, we show that this behavior can be obtained also for a Laplace operator on a periodic graph.
Source: Asymptotic Analysis
Authors: Pablo Miranda, Daniel Parra
Institutions: Universidad de Santiago de Chile, Universidad de La Frontera
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408618034