Limits in the characteristic-function description of non-Lindblad-type open quantum systems

In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized master equation containing a memory kernel which may lead to nonphysical time evolutions characterized by negative values of the density matrix diagonal elements [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)]. The main result of the paper is to demonstrate that there exist situations in which the symmetrically ordered characteristic function is perfectly well-defined while the corresponding density matrix loses positivity. Therefore, nonphysical situations may not show up in the characteristic function. As a consequence, the characteristic function cannot be considered an alternative complete description of the non-Lindblad dynamics.

Figure 1

Behavior of $\mid \chi \left({\mid \xi \mid }^2\right)\mid$, as given by Eq. (10), at different time instants in the interval $0<\tau <0$. The initial state is $\mid n=1⟩$ and $g∕\gamma =1$.