J L Lebowitz and L Pastur 2004 J. Phys. A: Math. Gen. 37 1517 doi:10.1088/0305-4470/37/5/004
A random matrix model of relaxation
J L Lebowitz1,2 and L Pastur3,4
Show affiliationsWe consider a two-level system, 
, coupled to a general n level system, 
, via a random matrix. We derive an integral representation for the mean reduced density matrix ρ(t) of 
in the limit n → ∞, and we identify a model of 
which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ(∞). We also consider 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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Issue 5 (6 February 2004)
Received 2 July 2003
Published 19 January 2004
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A random matrix model of relaxation
J L Lebowitz and L Pastur 2004 J. Phys. A: Math. Gen. 37 1517
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