Exact dynamics of moments of arbitrary order in the problems of open quantum systems theory

The report discusses the dynamics of moments of (bosonic or fermionic) creation and annihilation operators of arbitrary order for Gorini–Kossakowski–Sudarshan–Lindblad equations of a special form. Namely, the equations with quadratic generators and their averagings with respect to classical Levy fields, in particular with respect to Poisson and Wiener stochastic processes. We show that the dynamics of moments of creation and annihilation operators for arbitrary fixed order is fully defined by а solution of a closed system of finite number of ordinary differential equations.