We discuss the concept of discrete-scale invariance and how it leads to complex critical
exponents (or dimensions), ie to the log-periodic corrections to scaling. After their initial …

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the
connections between classical and quantum mechanics. It develops the relevant ideas of …

We investigate the pair correlation function of the sequence of fractional parts of α nd, n= 1,
2,…, N, where d≥ 2 is an integer and α an irrational. We conjecture that for badly …

The aim of these lectures is to present a résumé of some of the main ideas, assumptions and
results of the Wigner-Dyson type random matrix theories (RMT) which are relevant in the …

Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical
systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is …

We extend the results of two of our papers [Phys. Rev. A 94, 041603R (2016) and Phys. Rev.
B 97, 060303R (2018)] that touch upon the intimately connected topics of quantum chaos …

Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the
origin and has a piecewise C 1 boundary. For each integer Q≥ 1, we consider the integer …

From the viewpoint of eigenvalue level statistics, harmonic-oscillator systems are unusual.
Although integrable, these systems are nongeneric, and a spacing distribution does not exist …

The $\bm{n}$-point correlations between values of a linear form Page 1 Ergod. Th. & Dynam.
Sys. (2000), 20, 1127–1172 Printed in the United Kingdom c 2000 Cambridge University Press …

The Berry–Tabor conjecture asserts that local statistical measures of the eigenvalues λ j of a
“generic” integrable quantum system coincide with those of a Poisson process. We prove …