A random matrix model of relaxation
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 rgr(t) of \mathcal{S}_{2} in the limit n rarr infin, 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 rgr(infin). We also consider an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of rgr(t) on an appropriate time scale.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- February 2004
- DOI:
- 10.1088/0305-4470/37/5/004
- arXiv:
- arXiv:math-ph/0307004
- Bibcode:
- 2004JPhA...37.1517L
- Keywords:
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- Mathematical Physics;
- 82b31;
- 82c10
- E-Print:
- 20pages, LaTeX