%0 Journal Article %T Two-Time Correlation Functions in Dissipative and Interacting Bose¨CHubbard Chains %A Sandro Wimberger %A Zakari Denis %J Condensed Matter | An Open Access Journal from MDPI %D 2018 %R https://doi.org/10.3390/condmat3010002 %X Abstract A method is presented for the systematic derivation of a hierarchy of coupled equations for the computation of two-time correlation functions of operators for open many-body quantum systems. We show how these systems of equations can be closed in mean-field and beyond approximations. Results for the specific example of the spectral weight functions are discussed. Our method allows one to access the full temporal evolution, not just the stationary solution, of non-equilibrium open quantum problems described by a Markovian master equation. View Full-Tex %K open quantum systems %K Bose¨CEinstein condensates %K ultracold atoms %K correlation functions %K Green functions %U https://www.mdpi.com/2410-3896/3/1/2