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Updated: May 9, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Ergodicity and quantum correlations in irrational triangular billiards
T Araújo Lima1, S Rodríguez-Pérez, F M de Aguiar
1Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.
Abstract:
Pseudochaotic properties are systematically investigated in a one-parameter family of irrational triangular billiards (all angles irrational with π). The absolute value of the position correlation function C(x)(t) decays like ~t(-α). Fast (α≈1) and slow (0<α<1) decays are observed, thus indicating that the irrational triangles do not share a unique ergodic dynamics, which, instead, may vary smoothly between the opposite limits of strong mixing (α=1) and regular behaviors (α=0). Upgrading previous data, spectral statistical properties of the quantized counterparts are computed from 150000 energy eigenvalues numerically calculated for each billiard. Gaussian orthogonal ensemble spectral fluctuations are observed when α≈1 and intermediate statistics are found otherwise. Our irrational billiards have zero Kolmogorov-Sinai entropy and essentially infinity genus. Thus, differently from previous works on rational (pseudointegrable) enclosures, our results provide a missing classical-quantum correspondence regarding the ergodic hierarchy for a set of nonchaotic systems that might enjoy the strong mixing property.
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