Dynamical Systems Seminar: Exact local distribution of the absolutely continuous spectral measure

报告人： Xianzhe Li (Nankai University)
Time & Date: 14:00, April 1
地点： Room 1710

摘要： In this talk, we investigate the exact local distribution of the absolutely continuous spectral measures for analytic quasi-periodic Schrödinger operators. Building on quantitative almost reducibility, we derive asymptotic formulas for associated cocycle growth rates, and address the dynamical behavior of Schrödinger cocycles at energies exhibiting infinitely many Liouvillean frequency resonances. This enables us to determine the exact local distribution of spectral measures for the almost Mathieu operator in the subcritical regime (possessing purely absolutely continuous spectrum) at all energies. Furthermore, we provide a constructive method demonstrating that potentials exhibiting the same distributional behavior can densely exist within local energy regions.

Zoom Meeting ID: 844 0594 7424
Passcode: 076895