  Simulation and analysis of multidimensional dynamics of a quantum
non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has
proven to be an intuitive semiclassical approach to approximately solving the
dynamics of quantum systems. A Gaussian wavepacket approach is proposed for a
continuous space extension to the Hatano-Nelson model that enables transparent
analysis of the dynamics in terms of complex classical trajectories. We
demonstrate certain cases where the configuration space trajectory can be made
fully real by transforming the initial conditions to account for the
non-Hermiticity appropriately through the momentum coordinates. However, in
general the complex phase space is unavoidable. For the cases where the
trajectory is real, the effective force can be decomposed into that due to the
potential energy surface and that due to the imaginary vector potential. The
impact of the vector potential on the trajectory of the wavepacket is directly
proportional to both the strength of the vector potential and the width of the
wavepacket.
