Stochastic Master Equations in Thermal Environment

Stéphane Attal (1) , Clement Pellegrini (2)

1 ICJ - Institut Camille Jordan
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant.

Mots clés: retrun to equilibrium

Mots clés: Quantum trajectories; quantum thermal bath; retrun to equilibrium.

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]

Stéphane Attal, Clement Pellegrini. Stochastic Master Equations in Thermal Environment. Open Systems and Information Dynamics, 2010, 17 (4), pp.389-408. ⟨10.1142/S123016121000024⟩. ⟨hal-00863669⟩