On the Lyapounov exponents of Schrodinger operators associated with the standard map

TL;DR

This paper demonstrates that Schrödinger operators derived from the standard map exhibit positive mean Lyapunov exponents for almost all energies, indicating chaotic behavior in the quantum system.

Contribution

It establishes the positivity of Lyapunov exponents for Schrödinger operators linked to the standard map, a novel connection between dynamical systems and quantum operators.

Findings

Positive Lyapunov exponents for almost all energies

Chaotic behavior in quantum systems modeled by these operators

New insights into spectral properties of Schrödinger operators

Abstract

It is shown that Schrodinger operators defined from the standard map have positive (mean) Lyapounov exponents for almost all energies