DYNamical systems and non equilibrium states of complex SYStems : MATHematical methods and physical concepts


A thorough understanding of the behavior of complex systems is one of the main challenges for the physics of the twenty-first century. Even though a general theory is lacking so far, a set of common mathematical tools has been developed during recent years, offering a clue to interpret and find common patterns in the ample phenomenology exhibited by such systems. In this context our project is focused on investigating the rich properties of out-of-equilibrium systems by using both the standard statistical mechanics approach (from microscopic dynamics to macroscopic behavior) and a top-down one, consisting in the identification of universality classes as possible building blocks to unravel collective behavior. The aim of this project is devoted to the study of classical and quantum systems, both in the deterministic and the stochastic setting, with special emphasis on their transport properties and cooperative behavior. In particular, the latter point can be often associated with the presence of long range interactions, one of the unifying themes of our proposal. We foresee the use of analytical as well as numerical methods to study a wide class of models with applications ranging from gravitational systems, to social and economical phenomena and to biological complexes.