Distribution of time-constants for tunneling through a 1D Disordered Chain

TL;DR

This paper analyzes the statistical distributions of tunneling times and transmission in a disordered one-dimensional chain, revealing power-law behaviors linked to resonant tunneling through localized states.

Contribution

It provides the first detailed calculation of the distributions of transmission, delay, and transport times in 1D disordered chains, highlighting their power-law characteristics.

Findings

Distributions of T, Wigner delay time, and transport time have power-law forms.

Resonant tunneling through localized states explains the distribution shapes.

Results enhance understanding of electronic transport in disordered systems.

Abstract

The dynamics of electronic tunneling through a disordered 1D chain of finite length is considered. We calculate distributions of the transmission coefficient T, Wigner delay time and, $\tau_\phi$ and the transport time, $\tau_t=T\tau_\phi$. The central bodies of these distributions have a power-law form, what can be understood in terms of the resonant tunneling through localised states.