Many-boson dynamic correlations

In this paper we present an overview of a systematic development of the linear equations of motion for a dynamically correlated wave function that moves beyond the previous theories that include time-dependent pair correlations at most. We argue that these time-dependent pair correlations are insuficient to describe important physical effects in the energy/momentum regime of the He roton; minimally, time-dependent three-body correlations are necessary to capture the relevant physics. For simplicity we illustrate this on the problem of atomic impurities in He.