We propose an algebraic solution for a wide class of Lindblad-type master equations. Examples of dissipation in free field evolution, field evolution in the Kerr medium, two-photon field dissipation, atomic dissipation and two-mode field dissipation are given.
There are numerous examples in physics that can be modeled by the interaction between a small system of interest and a reservoir. The interaction typically leads to the irreversible decay of the system variables. As the system evolves into an equilibrium state, various parameters such as mean values, probabilities, and variances change until the final steady state is reached. The evolution of a system coupled to a reservoir with a short memory is often described by a master equation for the reduced density operator of the system. Master equations are important in physics because of their generality and hence wide range of applicability [1].
We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q -function, the average number of photons, and the distance between density matrices.