Open AccessNon-Equilibrium ϕ4 theory for networks: towards memory formations with quantum brain dynamics
Author(s) -
Akihiro Nishiyama,
Jack A. Tuszyński
Publication year - 2019
Publication title -
journal of physics communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.407
H-Index - 17
ISSN - 2399-6528
DOI - 10.1088/2399-6528/ab234d
Subject(s) - quantum decoherence , statistical physics , quantum , homogeneous , entropy (arrow of time) , physics , scalar field , quantum mechanics
We investigate the time evolution of quantum fields in neutral scalar ϕ 4 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.