Irreversibility in Paramagnetic Spin Systems. I. Kinetic Equations for the Reduced Density Matrices

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Abstract
Kinetic equations for the density matrix of weakly ordered paramagnetic spin systems are derived using the resummation procedure, introduced by Résibois and De Leener, for the formal solution of the Liouville-von Neumann equation. In the Weiss limit, this amounts to an explicit solution in terms of the spin autocorrelation functions which describe the dissipation in the system. The evolution equations so obtained are valid for both short and long times, and they may be solved by numerical methods without any phenomenological assumption.