Connection between the Schwinger–Keldysh Closed-Contour Approach and the Lindblad Master Equation

This chapter explores to what extent the closed-contour Schwinger–Keldysh approach and the Lindblad Master equation can be connected with each other. Here, the connection with the Schwinger–Keldysh closed-contour approach does not involve the full machinery of the Green’s functions method, but rather refers directly to the time evolution of the many-body density matrix, which contains a forward evolution operator from the reference time t ₀ to the measuring time t and a backward evolution operator from t back to t ₀. The key approximations to derive the Lindblad Master equation are specified in detail. As an example, a two-level system coupled to a phonon bath is explicitly considered.