Derivation of the Bloch-Redfield quantum master equation by Bogoliubov's method and generalization of the Born approximation

The choice between the Bloch-Redfield quantum master equation and various forms of the GKLS quantum master equations can be considered to be the main problem of the weak-coupling theory for open quantum systems. The Bloch-Redfield equation, being not of the GKLS form, predicts the unphysical behaviour, e.g., negative probabilities. In this talk, another view on the Bloch-Redfield equation will be given, which is based on the derivation of its equation by the Bogoliubov method. From this point of view, the Bloch-Redfield equation assumes not a product initial system-bath state (which is usually assumed in theory of open quantum systems), but a correlated initial system-bath state that is formed during their previous common evolution. This may explain unphysical predictions of this equations if we apply this equation to the product initial system-bath state. The talk is based on the paper A. S. Trushechkin, “Derivation of the Redfield Quantum Master Equation and Corrections to It by the Bogoliubov Method”, Proc. Steklov Inst. Math., 313 (2021), 246–257, arXiv: 2108.03128