In this paper, 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 [6], where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath has a 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.
@article{CML_2009__1_2_249_0,
author = {Nechita, Ion and Pellegrini, Cl\'ement},
title = {Quantum trajectories in random environment: the statistical model for a heat bath},
journal = {Confluentes Mathematici},
pages = {249--289},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {1},
number = {2},
year = {2009},
doi = {10.1142/S1793744209000109},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744209000109/}
}
TY - JOUR AU - Nechita, Ion AU - Pellegrini, Clément TI - Quantum trajectories in random environment: the statistical model for a heat bath JO - Confluentes Mathematici PY - 2009 SP - 249 EP - 289 VL - 1 IS - 2 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744209000109/ DO - 10.1142/S1793744209000109 LA - en ID - CML_2009__1_2_249_0 ER -
%0 Journal Article %A Nechita, Ion %A Pellegrini, Clément %T Quantum trajectories in random environment: the statistical model for a heat bath %J Confluentes Mathematici %D 2009 %P 249-289 %V 1 %N 2 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744209000109/ %R 10.1142/S1793744209000109 %G en %F CML_2009__1_2_249_0
Nechita, Ion; Pellegrini, Clément. Quantum trajectories in random environment: the statistical model for a heat bath. Confluentes Mathematici, Tome 1 (2009) no. 2, pp. 249-289. doi : 10.1142/S1793744209000109. http://www.numdam.org/articles/10.1142/S1793744209000109/
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