We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.

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Quantum fields with large degeneracy are often approximated as classical fields. Here, we show how quantum and classical evolution of a highly degenerate quantum field with repulsive contact self-interactions differ from each other. Initially, the field is taken to be homogeneous except for a small plane wave perturbations in only one mode. In quantum field theory, modes satisfying both momentum and energy conservation of the quasi-particles, grow exponentially with time. However, in the classical field approximation, the system is stable. We calculate the time scale after which the classical field description becomes invalid.

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