Non-equilibrium <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml38" display="inline" overflow="scroll" altimg="si38.gif"><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math> theory in open systems as a toy model of quantum field theory of the brain

Nishiyama, Akihiro; Tuszyński, Jack A.

doi:10.1016/j.aop.2018.09.009

Cited by 6 publications

(22 citation statements)

References 47 publications

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“…In figure 1, we show the central region and the N res reservoirs. (This is the generalization to the multiple reservoirs from the two reservoirs described previously [49][50][51][52][53] with tunneling effects [54][55][56][57]. )…”

Section: Time Evolution Equationsmentioning

confidence: 79%

“…In a similar way to [53], by use of the (C, C) component in the Kadanoff-Baym equations (15), we arrive at,…”

Section: Kinetic Entropy Current and The H-theoremmentioning

confidence: 97%

“…where m is the mass, λ C and λ α ʼs are coupling constants of the interaction, v α ʼs are tunneling coupling constants between the central region C and the reservoir α [49][50][51][52][53]. We shall adopt the closed time path formalism in figure 2, the Keldysh formalism [58,59], labelled by  to describe non-equilibrium phenomena, and use 2-Particle-Irreducible (2PI) effective action technique [60][61][62].…”

Section: Time Evolution Equationsmentioning

confidence: 99%

“…We neglect off-diagonal elements of the self-energy S, since they represent higher-order terms of tunneling coupling constants. Time evolution equations or solutions of each element of equation (15) are derived in a similar way to [53] by,…”

Section: Next We Derive the Kg Equations And The Kb Equations By Diffmentioning

confidence: 99%

“…We assume spatially homogeneous systems, which means that the condition of spatial homogeneity is satisfied for each system. The initial condition of the Green functions is the same as that in [53].…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Nishiyama

Tuszyński

2019

J. Phys. Commun.

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We investigate the time evolution of quantum fields in neutral scalar f 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.where water molecules' electric dipoles surrounding neurons become aligned in the same direction with the direction of the spontaneous breakdown of the rotational symmetry leading to a macroscopic ordered state. It has also been hypothesized that these coherent states might be specifically formed in the axonal and dendritic microtubule bundles which pack neuronal interiors in the brain [28]. Consequently, Nambu-Goldstone quanta emerging in the SSB effect, called polaritons, are absorbed into longitudinal modes of photons, and massive photons are created (via a Higgs mechanism). When photons acquire mass, they can stay in the coherent regions in the brain. In such situations they are called evanescent photons. The order parameters associated with this phenomenon are the coherent photon fields and the coherent charged Bose fields, which correspond to the mass of photons and the square root of the number of aligned dipoles. QBD describes several characteristic physical properties of memory, namely its diversity, long-term imperfect stability and nonlocality [6,7] and it does so by adopting unitarily inequivalent vacua in QFT. Vacua in QFT are different from those in quantum mechanics. Diverse unitarily inequivalent vacua in QFT appear due to the presence of an infinite number of the degrees of freedom of quantum fields [35]. Here, the term 'nonlocality' in QFT is distinguished from quantum nonlocality with entanglement. The dynamical order in the QFT system is maintained by massless quanta propagating in the whole coherent region, in which the propagation speed is consistent with the special theory of relativity. The size of each coherent region is on the order of 50 μm. Each memory is subdivided by coherent states distributed in several regions of the brain. In QBD, there are at least two types of quantum mechanisms of information transfer and integration among coherent regions. The first one is related to microtubules which connect two coherent regions [28]. Pulse propagation from one side (connected with one coherent state) to the other side (connected with the other) of microtubules can occur due to the self-induced transparency without the thermal loss of coherence since the time-scale of propagation is less than that of thermal interactions. What is required for this to occur i...

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Section: Time Evolution Equationsmentioning

confidence: 79%

“…In a similar way to [53], by use of the (C, C) component in the Kadanoff-Baym equations (15), we arrive at,…”

Section: Kinetic Entropy Current and The H-theoremmentioning

confidence: 97%

Section: Time Evolution Equationsmentioning

confidence: 99%

Section: Next We Derive the Kg Equations And The Kb Equations By Diffmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

See 3 more Smart Citations

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Nishiyama

Tuszyński

2019

J. Phys. Commun.

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Nonequilibrium quantum brain dynamics

Nishiyama

Tanaka

Tuszyński

2020

Quantum Boundaries of Life

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On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description

Mercado-Uribe

Guevara-Pantoja

García-Muñoz

et al. 2021

The Journal of Chemical Physics

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After exciting scientific debates about its nature, the development of the exclusion zone, a region near hydrophilic surfaces from which charged colloidal particles are strongly expelled, has been finally traced back to the diffusiophoresis produced by unbalanced ion gradients. This was done by numerically solving the coupled Poisson equation for electrostatics, the two stationary Stokes equations for low Reynolds numbers in incompressible fluids, and the Nernst–Planck equation for mass transport. Recently, it has also been claimed that the leading mechanism behind the diffusiophoretic phenomenon is electrophoresis [Esplandiu et al., Soft Matter 16, 3717 (2020)]. In this paper, we analyze the evolution of the exclusion zone based on a one-component interaction model at the Langevin equation level, which leads to simple analytical expressions instead of the complex numerical scheme of previous works, yet being consistent with it. We manage to reproduce the evolution of the exclusion zone width and the mean-square displacements of colloidal particles we measure near Nafion, a perfluorinated polymer membrane material, along with all characteristic time regimes, in a unified way. Our findings are also strongly supported by complementary experiments using two parallel planar conductors kept at a fixed voltage, mimicking the hydrophilic surfaces, and some computer simulations.

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Non-equilibrium ϕ4 theory in open systems as a toy model of quantum field theory of the brain

Cited by 6 publications

References 47 publications

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Nonequilibrium quantum brain dynamics

On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description

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Non-equilibrium ϕ4 theory in open systems as a toy model of quantum field theory of the brain

Cited by 6 publications

References 47 publications

Non-Equilibrium ϕ4 theory for networks: towards memory formations with quantum brain dynamics

Non-Equilibrium ϕ4 theory for networks: towards memory formations with quantum brain dynamics

Nonequilibrium quantum brain dynamics

On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description

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Product

Resources

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Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics