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Updated: Feb 19, 2026

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis
Published on: December 22, 2015
Signatures of chaos in the Brillouin zone
Aaron Barr1, Ariel Barr1, Max D Porter1
1Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
Abstract:
When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.
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