# Generalized Lyapunov exponent for the one-dimensional Schrödinger equation with Cauchy disorder: Some exact results

@article{Comtet2022GeneralizedLE,
title={Generalized Lyapunov exponent for the one-dimensional Schr{\"o}dinger equation with Cauchy disorder: Some exact results},
author={Alain Comtet and Christophe Texier and Yves Tourigny},
journal={Physical Review E},
year={2022}
}
• Published 4 October 2021
• Mathematics
• Physical Review E
We consider the one-dimensional Schrödinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function ψ(x), known in the literature as the generalized Lyapunov exponent; this is tantamount to studying the statistics of the so-called “finite size Lyapunov exponent”. The problem reduces to that of finding the leading eigenvalue of a certain non-random non-self-adjoint linear operator defined on a somewhat unusual space of functions. We focus…

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