Subcritical behavior for quasi-periodic Schrodinger cocycles with trigonometric potentials
We give a criterion implying subcritical behavior for quasi-periodic Schrodinger operators where the potential sampling function is given by a trigonometric polynomial. Subcritical behavior, in the sense of Avila's global theory, is known to imply purely absolutely continuous spectrum for all irrational frequencies and all phases.
Marx, Christoph A., Laura H. Shou, and Jake L. Wellens. 2018. "Subcritical behavior for quasi-periodic Schrodinger cocycles with trigonometric potentials." Journal of Spectral Theory 8(1): 123-163.
European Mathematical Society
Journal of Spectral Theory
Zero Lyapunov exponent, Avila global theory, Absolutely continuous spectrum