Seminarium Fizyki Materii Skondensowanej

Bogoliubov-Born-Green-Kirkwood-Yvon (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. Joint work with Leonardo Biagetti, Miłosz Panfil and Jacopo de Nardis.