A lower bound on the Lyapunov exponent for the generalized Harper's model

Svetlana Jitomirskaya; Wencai Liu

doi:10.1007/s10955-016-1543-7

paper

A lower bound on the Lyapunov exponent for the generalized Harper's model

arXiv:1611.10028 · doi:10.1007/s10955-016-1543-7

Abstract

We obtain a lower bound for the Lyapunov exponent of a family of discrete Schrödinger operators $(H u)_{n} = u_{n + 1} + u_{n - 1} + 2 a_{1} cos 2 π (θ + n α) u_{n} + 2 a_{2} cos 4 π (θ + n α) u_{n}$ , that incorporates both $a_{1}$ and $a_{2},$ thus going beyond the Herman's bound.

JSP

References in corpus (1)

Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials