  We develop a functional renormalization group approach to obtain the time
evolution of the momentum distribution function of interacting bosons out of
equilibrium. Using an external out-scattering rate as flow parameter, we derive
formally exact renormalization group flow equations for the non-equilibrium
self-energies in the Keldysh basis. A simple perturbative truncation of these
flow equations leads to an approximate solution of the quantum Boltzmann
equation which does not suffer from secular terms and gives accurate results
even for long times. We demonstrate this explicitly within a simple exactly
solvable toy model describing a quartic oscillator with off-diagonal pairing
terms.
