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arXiv · hep-ph/0401045

The effect of memory on relaxation in a scalar field theory

Takashi Ikeda
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Abstract

We derive a kinetic equation with a non-Markovian collision term which includes a memory effect, from Kadanoff-Baym equations in $ϕ^4$ theory within the three-loop level for the two-particle irreducible (2PI) 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 an influence of this effect on decay of a single particle excitation with zero momentum in 3+1 dimensions and the spatially homogeneous case. 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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Takashi Ikeda. 2004-01-09. The effect of memory on relaxation in a scalar field theory. https://doi.org/10.1103/physrevd.69.105018

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