During the last decade, many exciting phenomena have been experimentally observed and
theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid …

The most general and versatile defining feature of quantum chaotic systems is that they
possess an energy spectrum with correlations universally described by random matrix …

We derive expressions for the probability distribution of the ratio of two consecutive level
spacings for the classical ensembles of random matrices. This ratio distribution was recently …

We introduce a complex-plane generalization of the consecutive level-spacing ratio
distribution used to distinguish regular from chaotic quantum spectra. Our approach features …

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum
systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical …

Atomic and molecular samples reduced to temperatures below one microkelvin, yet still in
the gas phase, afford unprecedented energy resolution in probing and manipulating the …

A key goal of quantum chaos is to establish a relationship between widely observed
universal spectral fluctuations of clean quantum systems and random matrix theory (RMT) …

When classical systems fail to explore their entire configurational space, intriguing
macroscopic phenomena like aging and glass formation may emerge. Also closed quanto …

Motivated by recent experiments, we study the relaxation dynamics and thermalization in the
one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically …

Ultracold quantum gases serve as ideal models for the characterization of universal
properties of a variety of phenomena in quantum systems. In a formal analogy to …