Gaussian Ansatz Approach to the Driven Kerr Model

The proposed approach is based on the use of the generalized Kawasaki–Gunton projector, which approximates the density matrix by a chosen ansatz. In this work, we employ a Gaussian ansatz to describe the dynamics of the nonlinear Kerr model in the presence of an external field. Comparison with the analytical solution of the system without an external field regime, truncated to a two-level case, demonstrates good agreement. The evolution of the relevant expectation values is computed numerically for both weak and strong external fields. It is shown that applying Wick’s theorem corresponds only to the first-order approximation within our framework, whereas the proposed method provides systematic higher-order corrections.