Dynamical approach to chains of scatterers

TL;DR

This paper models linear chains of quantum scatterers as a discrete dynamical system, linking transport properties to spectral features and analyzing both single-channel and multi-channel cases through analytical and numerical methods.

Contribution

It introduces a dynamical systems framework for analyzing quantum scatterer chains, providing new insights into transport phenomena and spectral properties.

Findings

Transport properties relate to spectral features of scatterers.

Analytical solutions for translationally invariant chains.

Numerical analysis of multi-channel transport regimes.

Abstract

Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the transport through the chain to the spectral properties of individual scatterers. For a single-scattering channel case some new light is shed on known transport properties of disordered and noisy chains, whereas translationally invariant case can be studied analytically in terms of a simple deterministic dynamical map. The many-channel case was studied numerically by examining the statistical properties of scatterers that correspond to a certain type of transport of the chain i.e. ballistic or (partially) localised.