Weak-Coupling Master Equation

We explore the conditions under which, starting from a microscopic approach within the Nakajima–Zwanzig projection operator technique, a master equation leading to a Markov semigroup evolution for the reduced dynamics can be recovered. The obtained weak-coupling master equation has a number of interesting properties that will be investigated. We will consider in particular the case of a two-level system interacting with bosonic degrees of freedom, recovering the so-called quantum Bloch equations originated in the field of nuclear magnetic resonance and widely used in atomic physics and quantum optics. We will put into evidence typical quantum features emerging in this framework, such as the structure of the spectral peaks and photon anti-bunching in the light emitted by resonance fluorescence.