Andrea Trombettoni is a researcher at DEMOCRITOS, a CNR National Center for numerical simulations in condensed matter and nano-physics. The relations and collaborations between the CNR group and SISSA are an important factor for the success of the activity, since SISSA provides excellent scientific and computing facilities. Very important are also the relations with the International Centre of Theoretical Physics (ICTP) of Trieste, which regularly hosts visiting scientists and scientific conferences. The structure of the Research Unit foresees the participation of two CNR-IOM DEMOCRITOS researchers: Andrea Trombettoni and Federico Becca. A.T. has a long-standing expertise in the study of ultracold atoms and their use for implementing quantum Josephson devices. Since his PhD, he worked on the modelization of ultracold atoms setups for on-going experiments, joining theoretical aspects together with their concrete experimental counterpart. Federico Becca is a leading expert in the numerical analysis of strongly correlated systems: in the last years his activity focused on variational Monte Carlo approaches. The available computer programs are the result of years of development and are mainly written in optimized C++ and Fortran 90. All the applications are parallelized with MPI paradigm and can achieve an almost ideal scaling with the number of processors involved. Finally, the structure of the Unit foresees the hiring in Trieste of two Post-Docs on 3-year contracts. The activity of the CNR group will be complemented by the activity of two SISSA PhD students under the supervision of the coordinator of the Unit. The possibility to include other PhD students from SISSA working on the topics of the proposal is also foreseen.