the science

Funded by the European Union


The recent technological and experimental advances in the field of quantum simulation have led to the renaissance of the study of the dynamics of complex quantum systems. Different interdisciplinary approaches, ranging from condensed matter, high energy physics and quantum information, have emphasised the existence of constraints given by quantum mechanics on the time evolution of correlations and the transport properties. The purpose of this proposal is to tackle several issues at the intersection of these fields from the perspective of standard quantum statistical mechanics.

The scientific objectives

Generalized bounds on the Lyapunov exponents

So far, most of the attention of studies on quantum chaos has focused on the maximal Lyapunov exponent. Classically, however, that are several quantifiers to study chaotic dynamics. For instance, the generalised Lyapunov exponent (GLE) accounts for chaotic fluctuations of the dynamical system. Its non-trivial behaviour is associated with multifractality. This research objective is to derive bounds for the quantum GLE and to use them to study quantum multifractality. 

The physics of the bounds: 

from simple to complex models

In progress...

The bounds and quantum correlations

In progress...