Abstract
We show that the S-matrix for electrons propagating in a waveguide has different statistical properties depending on whether the waveguide cavity shape gives rise to chaotic or integrable behavior classically. We obtain distributions of energy level spacings for integrable and chaotic billiards shaped like the waveguide cavity. We also obtain distributions for Wigner delay times and resonance widths for the waveguide, for integrable and chaotic cavity geometries. Our results, obtained by direct numerical calculation of the electron wave function, are consistent with the predictions of random matrix theory.
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Akguc, G.B., Reichl, L.E. Conductance and Statistical Properties of Chaotic and Integrable Electron Waveguides. Journal of Statistical Physics 98, 813–834 (2000). https://doi.org/10.1023/A:1018683710779
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DOI: https://doi.org/10.1023/A:1018683710779