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From the early days of many-body physics, it was realized that theself-energy governs the relaxation or lifetime of the retarded Green$'$sfunction. So it seems reasonable to directly extend those results into thenonequilibrium domain. But experiments and calculations of the response ofquantum materials to a pump show that the relationship between the relaxationand the self-energy only holds in special cases. Experimentally, the decay timefor a population to relax back to equilibrium and the linewidth measured in alinear-response angle-resolved photoemission spectroscopy differ by largeamounts. Theoretically, aside from the weak-coupling regime where therelationship holds, one also finds deviations and additionally one seesviolations of Mathiessen$'$s rule. In this work, we examine whether looking atan effective transport relaxation time helps to analyze the decay times ofexcited populations as they relax back to equilibrium. We conclude that it maydo a little better, but it has a fitting parameter for the overall scale whichmust be determined.

Relaxation of nonequilibrium populations after a pump: the breaking of Mathiessen$'$s rule