Kinetic theory of long-range interacting quantum systems.

The approach to equilibrium in systems with strongly non-local interactions is known to exhibit a wide range of peculiar phenomena. One of its characteristic signatures is that, for many initial conditions, the system gets trapped in non-thermal configurations whose lifetime scales with the number of interacting constituents, referred to as quasi-stationary. While these phenomena are well captured in classical systems via the Vlasov hydrodynamic equation, their quantum counterpart is still lacking. In this work, we develop an effective hydrodynamic description for long-range interacting quantum systems by showing that, for such systems, the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy can be truncated, yielding a collisionless hydrodynamic equation analogous to the Vlasov equation. We demonstrate its applicability by studying the dynamics of long-range interacting one-dimensional spin chains and comparing the results with exact diagonalization techniques. We also discuss the role of quantum scars, which appear to be a universal feature of long-range interacting systems.