Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

By Ao Cai, C. Chavaudret, Jiangong You, Qi Zhou. Mathematische Zeitschrift, 2017

53 citations recorded by the source corpus.

We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $$C^{k}$$Ck quasi-periodic $$SL(2,{\mathbb {R}})$$SL(2,R) cocycle is 1 / 2-Hölder continuous in the almost reducible regime. As a consequence, we show that if the frequency is Diophantine, and the potential is small, then the integrated density of states of the corresponding quasi-periodic Schrödinger operator is 1 / 2-Hölder continuous.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/70bd42fe99f8bb43ff7258586aeda333530f8afd