Abstract
We derive a kinetic equation with a non-Markovian collision term that includes a memory effect from Kadanoff-Baym equations in ${\ensuremath{\varphi}}^{4}$ theory within the three-loop level for the two-particle irreducible effective action. The memory effect is incorporated into the kinetic equation by a generalized Kadanoff-Baym ansatz. Based on the kinetic equations with and without the memory effect, we investigate the influence of this effect on the decay of a single particle excitation with zero momentum in 3+1 dimensions and the spatially homogeneous case. The numerical results show that, while the time evolution of the zero mode is completely unaffected by the memory effect due to a separation of scales in the weak coupling regime, this effect leads first to faster relaxation than the case without it and then to slower relaxation as the coupling constant increases.
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