Winding number, density of states and acceleration
Mathematical Physics
2023-04-06 v1 Dynamical Systems
math.MP
Spectral Theory
Abstract
Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schr\"odinger operators, which reflect the asymptotic distribution of zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy respectively. We will prove that the winding number is in fact Avila's acceleration and it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schr\"odinger operators and Avila's global theory.
Keywords
Cite
@article{arxiv.2304.02486,
title = {Winding number, density of states and acceleration},
author = {Xueyin Wang and Zhenfu Wang and Jiangong You and Qi Zhou},
journal= {arXiv preprint arXiv:2304.02486},
year = {2023}
}