Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model

Details Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model

2010-10-05

arxiv.org/abs/1010.0751v3

Physics

Mathematical Physics

Scientific paper

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic $M_2(\mathbb{C})$-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Affiliated with

Also associated with

No associations

Rating

Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-85969