In my talk I will present a theoretical framework to study thermalisation phenomena in long-range interacting quantum gases. Our work is motivated by dipolar gas experiments performed in the group of Benjamin Lev. Our theory can be understood as a generalisation of famous Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy to systems close to integrability.

BBGKY hierarchy is a cornerstone of kinetic theory and can be understood as an exact representation of dynamics of many-particle system in terms of correlation functions. For weakly interacting systems, it can be efficiently truncated and leads to the standard results of kinetic theory: Landau and Boltzmann equations. In our work we extend this framework by considering quantum or classical many-body Hamiltonian systems, whose dynamics is given by an integrable, contact interactions, plus weak, long-range, two-body potential. Crucially, such systems are strongly correlated and integrable interactions are treated non-perturbatively. We show how the dynamics of local observables is given in terms of a generalised version of BBGKY hierarchy, which we denote as gBBGKY, which is built for the densities, and their correlations, of the quasiparticles of the underlying integrable model. We benchmark our formalism with exact simulations of long-range interacting hard rod gas and compare with experimental results for thermalisation process in dipolar 1D gases. Joint work with Leonardo Biagetti, Miłosz Panfil and Jacopo de Nardis.