Aspects of Open Quantum Dynamics

Abstract

Some aspects of open quantum dynamics are discussed. We make use of Lionville space notation {[}1], whereby operators are represented by `kets' and `bras', on which act superoperators (supops for short). We first derive in a concise way the complete positivity (CP) of `closed' dynamical semigroups, and the Kossakowski-Lindblad (KL) form of their generators {[}2]. The two main master equations, `memory' and `cumulant', are next derived {[}3]. It is emphasized that these two equations treated to a given order in the system-bath interaction amount to different approximations. This is illustrated with a `static' system in a thermal bath of oscillators with uncorrelated initial state {[}4], which also provides an instance of non-CP reduced dynamics. Finally we obtain the reduced Wigner function of an oscillator in a bath of oscillators, for arbitrary initial states. (Notation: We often write f (t) = f(t)).