2022/09/02 by Pablo Miranda, Miranda, Pablo, Daniel Parra +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2209.01246
openalex publication_date 2022/09/02 · openalex created_date 2022/09/08 · openalex updated_date 2026/07/28
In this article, we provide the spectral analysis of a Dirac-type operator on ℤ2 by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We prove that it remains bounded outside a single threshold and obtain its main asymptotic term in the unbounded case. Interestingly, we show that the constant in the main asymptotic term encodes the interaction between a flat band and whole non-constant bands. The strategy used is the reduction of the spectral shift function to the eigenvalue counting function of some compact operator which can be studied as a toroidal pseudo-differential operator.