Non-equilibrium Statistical Physics

A recent series of beautiful experiments with cold atomic gases has triggered a great deal of interest in some fundamental aspects of the non-equilibrium dynamics of correlated quantum systems. Due to the weak coupling with the environment, the phase coherence of these systems is preserved also for long times scales, allowing the experimental observation of the unitary evolution of an extended system.

The simplest example of non equilibrium dynamics is the quantum quench: an abrupt change in time of one parameter of the system or of its boundary conditions. Recent studies of quench dynamics in various strongly correlated models have demonstrated that the behavior of integrable and non-integrable systems can be quite different. Thermalisation can be observed, under specific circumstances, in nonintegrable systems: the asymptotic value of significant observables, such as the momentum distribution function, does not depend on the fine details of the initial state, but only on its energy. On the other hand, for integrable systems thermalisation does not seem to occur: a larger amount of information on the initial state seems necessary to predict the asymptotic state.

Our interest is to further explore the issue of thermalisation in integrable and non-integrable quantum models, taking advantage of analytical techniques as well as numerical simulations.


Non equilibrium dynamics can be also studied in the context of slow changes of the external parameters of a quantum system: this is the case of adiabatic dynamics. This kind of scenario is interesting from the point of view of quantum computation.Indeed adiabatic quantum computation schemes exploit the adiabatic theorem for reaching the solution of an optimization problem, by initially putting a system in its ground state and then changing adiabatically its Hamiltonian. The solution of the optimization problem can be encoded in the ground state of the final Hamiltonian, which can be reached by the system as long as there exists a finite gap between the ground and the first excited state, at every time of the evolution. Since critical system are characterized by the closure of the gap, it is very important to understand the behavior of quantum systems crossing phase transitions.