Abstract

This chapter is devoted to Lindblad master equation, obtained by a generalization of the quantum dynamic group to a time dependent semigroup. For this equation, we present a demonstration of Alicki and Lendi, obtained by a linear approximation of the openness operator, which describes the time evolution of a system of interest in an environment. We re-obtain this equation by taking the total dynamic equation with a bilinear dissipative potential in system and environment operators, and tracing over the environment states. In this way, we get physical expressions of the dissipation coefficients, as functions of the system operators. We present the quantum theory of Sandulescu and Scutaru, where the dissipative dynamics is described by friction and diffusion processes, with coefficients which satisfy fundamental constraints.