Disorder to chaos transition in the conductance distribution of corrugated waveguides

TL;DR

This study investigates how conductance distributions in corrugated waveguides transition from disorder-dominated to chaos-driven behavior as boundary complexity decreases, revealing a crossover from surface to bulk disorder effects.

Contribution

It demonstrates the disorder to chaos transition in conductance distribution of corrugated waveguides, connecting boundary complexity with transport regime changes.

Findings

Universal conductance distribution in diffusive and localized regimes.

Transition from surface to bulk disorder predictions at crossover.

Smooth boundaries lead to waveguides behaving as chains of chaotic cavities.

Abstract

We perform a detailed numerical study of the distribution of conductances $P(T)$ for quasi-one-dimensional corrugated waveguides as a function of the corrugation complexity (from rough to smooth). We verify the universality of $P(T)$ in both, the diffusive ($\bra T \ket> 1$) and the localized ($\bra T \ket\ll 1$) transport regimes. However, at the crossover regime ($\bra T \ket \sim 1$), we observe that $P(T)$ evolves from the surface-disorder to the bulk-disorder theoretical predictions for decreasing complexity in the waveguide boundaries. We explain this behavior as a transition from disorder to deterministic chaos; since, in the limit of smooth boundaries the corrugated waveguides are, effectively, linear chains of chaotic cavities.