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We derive an analytical expression of a Wigner function that approximatelydescribes the time evolution of the one-dimensional motion of a particle in anonharmonic potential. Our result provides an excellent approximation in theregime of wide potentials and small fluctuations, namely potentials that enablespatial expansions orders of magnitude larger than the one of the initial statebut that remain smaller compared to the relevant dynamical length scale (e.g.,distance between turning points). Our analytical result elucidates theinterplay between classical and quantum physics and the impact of decoherenceduring nonlinear dynamics. This analytical result is instrumental to design,optimize and understand proposals using nonlinear dynamics to generatemacroscopic quantum states of massive particles.

Wigner Analysis of Particle Dynamics in Wide Nonharmonic Potentials