Particle creation in nonstationary large N quantum mechanics

We consider an analog of particle production in a quartic \(O(N)\) quantum oscillator with time-dependent frequency, which is a toy model of particle production in the dynamical Casimir effect and de Sitter space. We calculate exact quantum averages, Keldysh propagator, and particle number using two different methods. First, we employ a kind of rotating wave approximation to estimate these quantities for small deviations from stationarity. Second, we extend these results to arbitrarily large deviations using the Schwinger-Keldysh diagrammatic technique. We show that in strongly nonstationary situations, including resonant oscillations, loop corrections to the tree-level expressions effectively result in an additional degree of freedom, \(N \to N + \frac{3}{2}\), which modifies the average number and energy of created particles.