  In this paper we develop high-order asymptotic-preserving methods for the
spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li
and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for
the classical inhomogeneous Boltzmann equation were constructed. A major
difficulty here is related to the non Gaussian steady states characterizing the
quantum kinetic behavior. We show that the proposed schemes work with
high-order accuracy uniformly in time for all Planck constants ranging from
classical regime to quantum regime, and all Knudsen numbers ranging from
kinetic regime to fluid regime. Computational results are presented for both
Bose gas and Fermi gas.
