Geodesic
Quantum trajectories in random environment: the statistical model for a heat bath
Confluentes Mathematici, Tome 1 (2009) no. 2, pp. 249-289

Voir la notice de l'article provenant de la source Numdam

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.

Publié le :
DOI : 10.1142/S1793744209000109

Nechita, Ion 1 ; Pellegrini, Clément 1

1 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :