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We propose a new method to study non-equilibrium dynamics of scalar fieldsstarting from non-Gaussian initial conditions using Keldysh field theory. Weuse it to study dynamics of phonons coupled to non-interacting bosonic andfermionic baths, starting from initial Fock states. We find that in onedimension long wavelength phonons coupled to fermionic baths do not thermalizeboth at low and high bath-temperatures. At low temperature, constraints fromenergy-momentum conservation lead to a narrow bandwidth of particle-holeexcitations and the phonons effectively do not see this bath. On the otherhand, the strong band-edge divergence of the particle-hole density of statesleads to an undamped polariton-like mode of the dressed phonons above the bandedge of the particle-hole excitations. These undamped modes contribute to thelack of thermalization of long wavelength phonons at high temperatures. Inhigher dimensions, these constraints and the divergence of density of statesare weakened and lead to thermalization at all wavelengths.

Non-equilibrium scalar field dynamics starting from Fock states: Absence of thermalization in one dimensional phonons coupled to fermions