Disorder to chaos transition in the conductance distribution of corrugated waveguides

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.