Signum Function Method for Generation of Correlated Dichotomic Chains

TL;DR

This paper investigates a signum-function-based method for generating correlated binary sequences with specific properties, useful in designing materials like superlattices and waveguides with tailored transport characteristics.

Contribution

It introduces a novel approach to construct binary sequences with prescribed correlations using Fourier transform techniques, expanding capabilities in material design.

Findings

Conditions for constructing binary sequences with desired correlations

Method applicability in superlattice and waveguide design

Potential for controlling transport properties in engineered materials

Abstract

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.