Regular Article

One dimensional localization for arbitrary disorder correlations^★

¹ Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
² College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, United Arab Emirates
³ Department of Physics, McGill University, Montréal, QC H3A 2T8, Canada
⁴ Center for the Physics of Materials (CPM), McGill University, Montreal, QC H3A 2T8, Canada

^a e-mail: hilke@physics.mcgill.ca

Received: 30 September 2019
Received in final form: 4 November 2019
Published online: 11 December 2019

Abstract

We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation and calculate all the correlators needed for the localization length expression. We compare our results with numerical results for the special case, where the autocorrelation decays quadratically with distance. We look at disorder ranging from weak to strong disorder, which shows excellent agreement. For the numerical simulation, we introduce a generic method to obtain a random potential with an arbitrary autocorrelation function. The correlated potential is obtained in terms of the convolution between a Wiener stochastic potential and a function of the correlation.