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We simulate a free dissipative and coherent-driven Kerr nonlinear system using a time-evolving block decimation (TEBD) algorithm to study the impact of the initial state on the exact quantum dynamics of the system. The superposition of two coherent branches results in non-classical time dynamics. The Wigner state representation confirms that the system ends up saturating to two different branches, through evolving different trajectories, resulting in de-Gaussification throughout evolution. Furthermore, we also see that the time evolution suffers the residual effect of the initial state.
Souvik Agasti (Thu,) studied this question.