Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup>
We derive time evolution equations, namely the Schrödinger-like equations and the Klein−Gordon equations for coherent fields and the Kadanoff−Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in <inline-formula> &l...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-10-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/21/11/1066 |
| _version_ | 1798038738580799488 |
|---|---|
| author | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski |
| author_facet | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski |
| author_sort | Akihiro Nishiyama |
| collection | DOAJ |
| description | We derive time evolution equations, namely the Schrödinger-like equations and the Klein−Gordon equations for coherent fields and the Kadanoff−Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> dimensions. Next we introduce a kinetic entropy current based on the KB equations in the first order of the gradient expansion. We show the H-theorem for the leading-order self-energy in the coupling expansion (the Hartree−Fock approximation). We show conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to quantum brain dynamics, that is QED, with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain. |
| first_indexed | 2024-04-11T21:44:22Z |
| format | Article |
| id | doaj.art-cfd7ebc4c210433996bae6263a6b7a24 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T21:44:22Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cfd7ebc4c210433996bae6263a6b7a242022-12-22T04:01:28ZengMDPI AGEntropy1099-43002019-10-012111106610.3390/e21111066e21111066Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup>Akihiro Nishiyama0Shigenori Tanaka1Jack A. Tuszynski2Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan;Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan;Department of Oncology, University of Alberta, Cross Cancer Institute, Edmonton, AB T6G 1Z2, CanadaWe derive time evolution equations, namely the Schrödinger-like equations and the Klein−Gordon equations for coherent fields and the Kadanoff−Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> dimensions. Next we introduce a kinetic entropy current based on the KB equations in the first order of the gradient expansion. We show the H-theorem for the leading-order self-energy in the coupling expansion (the Hartree−Fock approximation). We show conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to quantum brain dynamics, that is QED, with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.https://www.mdpi.com/1099-4300/21/11/1066non-equilibrium quantum field theoryquantum brain dynamicskadanoff–baym equationentropysuper-radiance |
| spellingShingle | Akihiro Nishiyama Shigenori Tanaka Jack A. Tuszynski Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> Entropy non-equilibrium quantum field theory quantum brain dynamics kadanoff–baym equation entropy super-radiance |
| title | Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> |
| title_full | Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> |
| title_fullStr | Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> |
| title_full_unstemmed | Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> |
| title_short | Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 21 Dimensions<sup>+</sup> |
| title_sort | non equilibrium quantum brain dynamics super radiance and equilibration in 21 dimensions sup sup |
| topic | non-equilibrium quantum field theory quantum brain dynamics kadanoff–baym equation entropy super-radiance |
| url | https://www.mdpi.com/1099-4300/21/11/1066 |
| work_keys_str_mv | AT akihironishiyama nonequilibriumquantumbraindynamicssuperradianceandequilibrationin21dimensionssupsup AT shigenoritanaka nonequilibriumquantumbraindynamicssuperradianceandequilibrationin21dimensionssupsup AT jackatuszynski nonequilibriumquantumbraindynamicssuperradianceandequilibrationin21dimensionssupsup |