  We study the out-of-equilibrium evolution of an O(2)-invariant scalar field
in which a conserved charge is stored. We apply a loop expansion of the
2-particle irreducible effective action to 3-loop order. Equations of motion
are derived which conserve both total charge and total energy yet allow for the
effects of scattering whereby charge and energy can transfer between modes.
Working in (1+1)-dimensions we solve the equations of motion numerically for a
system knocked out of equilibrium by a sudden temperature quench. We examine
the initial stages of the charge and energy redistribution. This provides a
basis from which we can understand the formation of Bose-Einstein condensates
from first principles.
