  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.
