  We introduce a numerical method to simulate nonlinear open quantum dynamics
of a particle in situations where its state undergoes significant expansion in
phase space while generating small quantum features at the phase-space Planck
scale. Our approach involves simulating the Wigner function in a time-dependent
frame that leverages information from the classical trajectory to efficiently
represent the quantum state in phase space. To demonstrate the capabilities of
our method, we examine the open quantum dynamics of a particle evolving in a
one-dimensional weak quartic potential after initially being ground-state
cooled in a tight harmonic potential. This numerical approach is particularly
relevant to ongoing efforts to design, optimize, and understand experiments
targeting the preparation of macroscopic quantum superposition states of
massive particles through nonlinear quantum dynamics.
