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A Matrix Model of Relaxation

J. L. Lebowitz·L. Pastur
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Abstract

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 $ρ (t)$ 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 $ρ (\infty)$. We consider also an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of $ρ(t)$ on an appropriate time scale.

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J. L. Lebowitz, L. Pastur. 2003-07-02. A Matrix Model of Relaxation. https://doi.org/10.1088/0305-4470/37/5/004

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