title: Ergodicity and quantum correlations in irrational triangular billiards.
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.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.
authors.forename: T
authors.initials: T
authors.lastname: Araújo Lima
authors.forename: S
authors.initials: S
authors.lastname: Rodríguez-Pérez
authors.forename: F M
authors.initials: FM
authors.lastname: de Aguiar