Boost-invariant quantum evolution of a meson field at large proper times

We construct asymptotic solutions of the functional Schr{umlt o}dinger equation for a scalar field in the Gaussian approximation at large proper times. These solutions describe the late proper time stages of the expansion of a meson gas with boost-invariant boundary conditions. The relevance of these solutions for the formation of a disoriented chiral condensate in ultrarelativistic collisions is discussed. {copyright} {ital 1997} {ital The American Physical Society}