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The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field

Received: 25 January 2023     Accepted: 20 February 2023     Published: 31 March 2023
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Abstract

The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (TFD) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (TFD) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (TFD) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.

Published in American Journal of Physics and Applications (Volume 11, Issue 1)
DOI 10.11648/j.ajpa.20231101.13
Page(s) 21-30
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Entanglement, Equilibrium and Non-equilibrium Thermodynamic State, Electron-two Harmonic Oscillators

References
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  • APA Style

    Ahlem Abidi. (2023). The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field. American Journal of Physics and Applications, 11(1), 21-30. https://doi.org/10.11648/j.ajpa.20231101.13

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    ACS Style

    Ahlem Abidi. The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field. Am. J. Phys. Appl. 2023, 11(1), 21-30. doi: 10.11648/j.ajpa.20231101.13

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    AMA Style

    Ahlem Abidi. The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field. Am J Phys Appl. 2023;11(1):21-30. doi: 10.11648/j.ajpa.20231101.13

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  • @article{10.11648/j.ajpa.20231101.13,
      author = {Ahlem Abidi},
      title = {The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field},
      journal = {American Journal of Physics and Applications},
      volume = {11},
      number = {1},
      pages = {21-30},
      doi = {10.11648/j.ajpa.20231101.13},
      url = {https://doi.org/10.11648/j.ajpa.20231101.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20231101.13},
      abstract = {The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (TFD) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (TFD) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (TFD) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.},
     year = {2023}
    }
    

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    T1  - The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field
    AU  - Ahlem Abidi
    Y1  - 2023/03/31
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ajpa.20231101.13
    DO  - 10.11648/j.ajpa.20231101.13
    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
    SP  - 21
    EP  - 30
    PB  - Science Publishing Group
    SN  - 2330-4308
    UR  - https://doi.org/10.11648/j.ajpa.20231101.13
    AB  - The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (TFD) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (TFD) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (TFD) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.
    VL  - 11
    IS  - 1
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Author Information
  • Research Unit of Nuclear Physics and High Energies, Faculty of Sciences of Tunis, Tunis El Manar University, Tunis, Tunisia

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