Transmission distribution, P(\ln T), of 1D disordered chain: low-T tail

TL;DR

This paper shows that the low-transmission tail in 1D disordered chains depends strongly on the correlation radius of the potential, affecting the shape and nature of the disorder configurations responsible for low transmission.

Contribution

It reveals how the correlation radius influences the phase volume of trapping configurations, altering the shape of the transmission distribution tail from Gaussian to exponential.

Findings

The tail shape depends on the correlation radius even when much shorter than the wavelength.

The phase volume restriction changes the disorder configurations from Bragg mirrors to loose mirrors.

The distribution tail transitions from Gaussian to exponential with increasing phase-volume restriction.

Abstract

We demonstrate that the tail of transmission distribution through 1D disordered Anderson chain is a strong function of the correlation radius of the random potential, $a$, even when this radius is much shorter than the de Broglie wavelength, $k_F^{-1}$. The reason is that the correlation radius defines the phase volume of the trapping configurations of the random potential, which are responsible for the low-$T$ tail. To see this, we perform the averaging over the low-$T$ disorder configurations by first introducing a finite lattice spacing $\sim a$, and then demonstrating that the prefactor in the corresponding functional integral is exponentially small and depends on $a$ even as $a \to 0$. Moreover, we demonstrate that this restriction of the phase volume leads to the dramatic change in the shape of the tail of ${\cal P}(\ln T)$ from universal Gaussian in $\ln T $ to a simple exponential (in $\ln T $) with exponent depending on $a$. Severity of the phase-volume restriction affects the shape of the low-$T$ disorder configurations transforming them from almost periodic (Bragg mirrors) to periodically-sign-alternating (loose mirrors).