  We simulate coherent driven free dissipative Kerr nonlinear system
numerically using time evolving block decimation (TEBD) algorithm and time
propagation on the Heisenberg equation of motion using Eulers method to study
how the numerical results are analogous to classical bistability. The system
evolves through different trajectories to stabilize different branches for
different external drives and initial conditions. The Wigner state reprentation
confirms the system to suffer a residual effect of initial state throughout the
non-classical dynamical evolution and the steady state of the system.
Furthermore, we also see the numerically simulated spectral density remains
significantly different from analytical counterparts when initial states do not
lie to the same branch of the final state.
