Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

The conductance of a waveguide containing a finite number of periodically placed identical pointlike impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-Büttiker formula. For a large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands times the universal constant ${2e}^2/h.\mathrm{}$ This lower value is reached exponentially with the increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum chaotic. The conductance, in units of ${2e}^2/h,$ changes from $N$ corresponding to the empty waveguide to $\sim N/2\mathrm{}$ corresponding to a chaotic or disordered system. The conductance can be expressed as $2e(1-c/2)N,$ where the parameter $0<c<\mathrm{}1\mathrm{}$ measures the chaoticness of the system.