Self-similarity in nonclassical transmission through a fibonacci sequence of Gaussian barriers

Abstract

We study quantum mechanical scattering by one-dimensional sequence of Gaussian barriers and calculate the transmission through such systems. We illustrate the physical aspects of resonance states and their coupling with the example of two and three barriers. Finally, we consider Fibonacci sequences of such barriers to demonstrate the properties of scaling, multifractality and self-similarity. These results are compared with those of periodic structures. All the calculations are based on the transfer matrix approach resulting from a fine segmentation of each barrier.