Theory of semi-ballistic wave propagation

TL;DR

This paper develops a theoretical framework for semi-ballistic wave propagation in disordered systems, analyzing scattering effects beyond the second order Born approximation and comparing predictions with numerical and experimental data.

Contribution

It introduces a comprehensive theory for semi-ballistic wave transport, including geometric resonances for attractive scatterers and analytical solutions for various geometries.

Findings

Attractive point scatterers exhibit geometric resonances.

Analytical transport equations are derived for long samples.

Predictions align well with numerical and experimental results.

Abstract

Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much scattering that the transport is diffusive. For such systems randomness is modelled by an inhomogeneous density of point-like scatterers. These are first considered in the second order Born approximation and then beyond that approximation. In the latter case it is found that attractive point scatterers in a cavity always have geometric resonances, even for Schr\"odinger wave scattering. In the long sample limit the transport equation is solved analytically. Various geometries are considered: waveguides, films, and tunneling geometries such as Fabry-P\'erot interferometers and double barrier quantum wells. The predictions are compared with new and existing numerical data and with experiment. The agreement is quite satisfactory.