Abstract
We investigate the time evolution of quantum fields in neutral scalar ϕ4 theory for open systems with the central region and the multiple reservoirs (networks) as a toy model of quantum field theory of the brain. First we investigate the Klein–Gordon (KG) equations and the Kadanoff–Baym (KB) equations in open systems in d + 1 dimensions. Next, we introduce the kinetic entropy current and provide the proof of the H-theorem for networks. Finally, we solve the KG and the KB equations numerically in spatially homogeneous systems in 1 + 1 dimensions. We find that decoherence, entropy saturation and chemical equilibration all occur during the time evolution in the networks. We also show how coherent field transfer takes place in the networks.
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