Superadiabatic basis in cosmological particle production: Application to preheating

We discuss the adiabatic basis dependence of particle number in time-dependent backgrounds. In particular, we focus on preheating after inflation, and show that, for the optimal basis, the time dependence of the produced particle number can be well approximated by a simple connection formula, which can be obtained by analysing Stokes phenomenon in given backgrounds. As we show explicitly, the simple connection formula can describe various parameter regions such as narrow and broad resonance regime in a unified manner.