interactions between a system and a thermal bath(∗)

Summary. — The time evolution equation of the reduced density matrix of a quan-tum system composed of one or many particles subjected to a conservative force field and interacting with a thermal bath has been derived. This result is achieved by analogy with classical models based upon the Langevin and Fokker-Planck equa-tions. According to the Langevin approach, the interaction is modelled by means of a random force field and a viscous friction term. We generalise this classical approach introducing suitable operators that describe the quantum evolution of a system weakly coupled to a thermal bath. In particular, we define a kind of friction operator that can be thought as the quantal counterpart of the classical Langevin term corresponding to the viscous force. The proposed approach has the invaluable advantage of yielding a handy differential equation to model the quantum interaction between a system and a thermal bath. PACS 42.50.Lc – Quantum fluctuations, quantum noise, and quantum jumps. PACS 05.30 – Quantum statistical mechanics. PACS 05.70.Ln – Nonequilibrium and irreversible thermodynamics