Markovian Properties of the Pauli Fierz model

The Hamiltonian approach of the Pauli-Fierz model is studied by Derezinski and Jaksic (cf. [7]). In this paper, we give the Markovian description of this model. Using the weak coupling limit, we derive the quantum Markovian semigroup of the Pauli-Fierz system from its Hamiltonian description. Also, we give the explicit form of the associated Lindblad generator. As a consequence, we study the properties of the associated quantum master equation: Quantum detailed balance condition and return to equilibrium. Finally, we give the associated quantum Langevin equation which can be obtained by a repeated quantum interaction Hamiltonian.