Network techniques for interaction quenches
Understanding the universal features of the non-equilibrium dynamics 
of strongly interacting one-dimensional quantum many-body systems 
is one of the most challenging and intriguing aspect of the recent researches  
in the broad domain of the quantum many-particle physics.
In this project one merges analytical with numerical methods in order to explore 
the exotic behavior of interacting quantum models when brought out-of-equilibrium.
Indeed, although the equilibrium properties of quantum systems could be understood
in terms of standard approaches, away from the equilibrium a complete understanding is still missing.
In particular, the project aims to fill the lack of knowledge still present in this exciting domain, 
pursuing two main ideas: (i) The development of new numerical methods based on tensor-network
techniques, so as to explore the post-quench dynamics in closed quantum systems; 
with a special attention to the very recent continuous version of such algorithms.
(ii) A better theoretical understanding (strongly supported by the numerical approach in (i)) 
of the effects of symmetry breaking, interactions and integrability, in the non-equilibrium dynamics; 
especially with respect to the non-equilibrium transport of energy and particle throughout the systems as well as
a universal description of the stationary states (both equilibrium and non-equilibrium) that 
emerge at late times. 
Beside its conceptual importance, a complete universal characterization of the non-equilibrium dynamics
of 1D quantum systems will have various application in quantum engineering, being a
crucial step forward to construct a quantum computer.