Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath

Ion Nechita (1, 2) , Clément Pellegrini (3)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics and Statistics [Ottawa]
3 School of Physics and National Institue for Theoretical Physics

In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated measurements. Physically, they describe the evolution of a small system in contact with a heat bath undergoing continuous measurement. The equations obtained in the present work are qualitatively different from the ones derived in \cite{A1P1}, where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath provides clear physical interpretation in terms of emissions and absorptions of photons. Our approach yields models of random environment and unravelings of stochastic master equations. The equations are rigorously obtained as solutions of martingale problems using the convergence of Markov generators.

Mots clés: Quantum trajectory; stochastic differential equation; stochastic Schrodinger equation

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

Ion Nechita, Clément Pellegrini. Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath. Confluentes Mathematici, 2009, 1 (2), pp.249-289. ⟨10.1142/S1793744209000109⟩. ⟨hal-00410291⟩