Classical Aspects of Quantum Fields Far from Equilibrium

We consider the time evolution of nonequilibrium quantum scalar fields in the $O\left(N\right)$ model, using the next-to-leading order $1/N$ expansion of the two-particle irreducible effective action. A comparison with exact numerical simulations in $1+1$ dimensions in the classical limit shows that the $1/N$ expansion gives quantitatively precise results already for moderate values of $N$. For sufficiently high initial occupation numbers the time evolution of quantum fields is shown to be accurately described by classical physics. Eventually the correspondence breaks down due to the difference between classical and quantum thermal equilibrium.