  The aim of this paper is two-fold. First, we present a phase space
perspective on long range double ionization in a one dimensional model of
helium. The dynamics is simulated with the periodic von Neumann (PvB) method,
an exact quantum method based on a lattice of phase space Gaussians. Second, we
benchmark the method by comparing to the Multiconfiguration Time-dependent
Hartree method. The PvB approach is found to be faster than the standard MCTDH
code for the dynamics calculations and to give better accuracy control.
