One Dimensional Localization for Arbitrary Disorder Correlations

TL;DR

This paper develops a method to evaluate the localization length of waves in one-dimensional disordered systems with arbitrary autocorrelation functions, extending beyond the Born approximation and validating with numerical simulations.

Contribution

It introduces a non-linear approximation for localization length calculation and a generic method to generate correlated random potentials for arbitrary autocorrelations.

Findings

Excellent agreement between theory and numerical results for quadratic autocorrelation decay.

Method effectively handles weak to strong disorder regimes.

Provides a versatile approach for modeling correlated disorder in 1D systems.

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.