Title: Simulation of Kerr Nonlinearity: Revealing Initial State Dependency

Abstract: 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.