Particle creation in nonstationary large N quantum mechanics

TL;DR

This paper investigates particle creation in a time-dependent large N quantum oscillator model, providing exact calculations and revealing how strong nonstationarity affects particle number and energy through loop corrections.

Contribution

It introduces a detailed analysis of particle production in a nonstationary quantum oscillator, extending results to large deviations and uncovering a modified effective degree of freedom.

Findings

Loop corrections increase effective N by 1.5 in nonstationary regimes

Exact quantum averages and propagators are computed for the model

Resonant oscillations significantly enhance particle production

Abstract

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.