Winding Number, Density of States, and Acceleration

Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schrodinger 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, it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schrodinger operators and Avila's global theory.Communicating Editor: Prof Svetlana Jitomirskaya