Prof. Dr. Tomaž Prosen (FMF): Quantum Many Body Chaos
Quantum chaos (of mostly single particle problems) has been a fruitful interdisciplinary arena of research in 1980sâ and 1990sâ. In recent years, the field has dramatically revived around the quantum many-body problem gathering very diverse communities of theoretical physicists ranging from condensed matter, quantum optics and quantum information, to quantum gravity. One of the most general characteristics of quantum chaotic systems is the ubiquitous applicability of random matrix theory.
After a general introduction to the field, I will focus specifically on the fascinating problem of 'unreasonable effectiveness' of random matrix theory for description of spectral fluctuations in extended quantum lattice systems. A class of locally interacting spin systems has been recently identified where the fundamental measure of (quasi)energy level fluctuations, the spectral form factor, is proven to match with random matrix theory, and where spatiotemporal correlation functions of local observables as well as some measures of dynamical complexity can be calculated analytically. These, so-called dual unitary systems, include the whole 'ergodic hierarchy' of dynamics: integrable, non-ergodic, ergodic, and generically, (maximally) chaotic cases.