  We study in detail (p)reheating after multi-field inflation models with a
particular focus on N-flation. We consider a variety of different couplings
between the inflatons and the matter sector, including both quartic and
trilinear interactions with a light scalar field. We show that the presence of
multiple oscillating inflatons makes parametric resonance inefficient in the
case of the quartic interactions. Moreover, perturbative processes do not
permit a complete decay of the inflaton for this coupling. In order to recover
the hot big bang, we must instead consider trilinear couplings. In this case we
show that strong nonperturbative preheating is possible via multi-field
tachyonic resonance. In addition, late-time perturbative effects do permit a
complete decay of the condensate. We also study the production of gauge fields
for several prototype couplings, finding similar results to the trilinear
scalar coupling. During the course of our analysis we develop the mathematical
theory of the quasi-periodic Mathieu equation, the multi-field generalization
of the Floquet theory familiar from preheating after single field inflation. We
also elaborate on the theory of perturbative decays of a classical inflaton
condensate, which is applicable in single-field models also.
