Chaos and integrability in triangular billiards
Abstract
We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy eigenstate localisation in the Krylov basis, and (5) dynamical growth of spread complexity. The billiards we study are classified as integrable, pseudointegrable or nonintegrable, depending on their internal angles which determine properties of classical trajectories and associated quantum spectral statistics. A consistent picture emerges when transitioning from integrable to nonintegrable triangles: (1) LSRs increase; (2) spectral complexity growth slows down; (3) Lanczos coefficient variances decrease; (4) energy eigenstates delocalize in the Krylov basis; and (5) spread complexity increases, displaying a peak prior to a plateau instead of recurrences. Pseudointegrable triangles deviate by a small amount in these charactertistics from nonintegrable ones, which in turn approximate models from the Gaussian Orthogonal Ensemble (GOE). Isosceles pseudointegrable and nonintegrable triangles have independent sectors that are symmetric and antisymmetric under a reflection symmetry. These sectors separately reproduce characteristics of the GOE, even though the combined system approximates characteristics expected from integrable theories with Poisson distributed spectra.
 Publication:

arXiv eprints
 Pub Date:
 July 2024
 DOI:
 10.48550/arXiv.2407.11114
 arXiv:
 arXiv:2407.11114
 Bibcode:
 2024arXiv240711114B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 25 pages, 12 figures