Spin Relaxation: The Multiple-Time-Scale Point of View

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Abstract
The linear (Redfield) form of the equation of motion for the density matrix of a spin system immersed in a heat bath is derived. The usual derivations employ perturbation theory which suffers from the presence of secular terms familiar from nonlinear mechanics. We employ the multiple‐time‐scale technique as developed by Frieman and Sandri to eliminate the secular terms and render the expansions valid for all time. The method introduces explicit time variables to exploit the multiplicity of time scales inherent to the problem.