A Matrix Model of Relaxation
Lebowitz, J. L. ; Pastur, L.
arXiv, 0307004 / Harvested from arXiv
We consider a two level system, $\mathcal{S}_{2}$, coupled to a general $n$ level system, $\mathcal{S}_{n}$, via a random matrix. We derive an integral representation for the mean reduced density matrix ${\rho} (t)$ of $\mathcal{S}_{2}$ in the limit $n\to \infty $, and we identify a model of $\mathcal{S}_{n}$ which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ${\rho} (\infty)$. We consider also an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of $\rho (t)$ on an appropriate time scale.
Publié le : 2003-07-02
Classification:  Mathematical Physics,  82b31,  82c10
@article{0307004,
     author = {Lebowitz, J. L. and Pastur, L.},
     title = {A Matrix Model of Relaxation},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0307004}
}
Lebowitz, J. L.; Pastur, L. A Matrix Model of Relaxation. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307004/