Particle creation in a toy nonstationary model

In some interacting nonstationary systems, correlation functions receive secularly growing loop corrections that cannot be resummed with an analogue of the kinetic equation. In particular, such a secular growth is observed for the dynamical Casimir effect and for light fields in de Sitter space. I will consider one of the simplest examples of such a system — a system of N coupled quantum mechanical oscillators with time-dependent frequency and O(N)-symmetric quartic interaction. Using two different methods, I will calculate the exact quantum averages, the Keldysh propagator, and the total excitation energy in the large N limit. As a result, I will show that in highly nonstationary situations, loop corrections to the tree-level expressions effectively result in an additional degree of freedom, N→N+3/2, which modifies the expression for the average excitation energy.