International Journal of Applied Mathematics and Theoretical Physics

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Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate

Received: Jan. 10, 2023    Accepted: Mar. 07, 2023    Published: Mar. 20, 2023
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Abstract

This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first one, represented by a Fermi energy with a value of - 0.4 meV, where the rest of the material parameters, and the degrees of freedom of the normal to the superconducting phase transition are not sensitive to the self-consistent variation of the zero temperature superconducting energy gap. A different case is found when in the self-consistent numerical procedure, the Fermi energy takes a value of - 0.04 meV, indicating that the fermion-dressed quasiparticles have material parameters strongly sensitive to the numerical changes in the zero temperature gap, resulting in a reduced phase space, where the input and output zero superconducting energy values, and the degrees of freedom are separated by the self-consistent numerical analysis. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.

DOI 10.11648/j.ijamtp.20230901.11
Published in International Journal of Applied Mathematics and Theoretical Physics ( Volume 9, Issue 1, March 2023 )
Page(s) 1-13
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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), 2024. Published by Science Publishing Group

Keywords

Strontium-Doped Lanthanum Cuprate, Reduce Phase Space, Configuration Space, Phase Space, Zero Temperature Elastic Scattering Cross-Section, Lifetime, Mean Free Path, Numerical Modelling

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    Pedro Contreras, Dianela Osorio, Anjna Devi. (2023). Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate. International Journal of Applied Mathematics and Theoretical Physics, 9(1), 1-13. https://doi.org/10.11648/j.ijamtp.20230901.11

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    ACS Style

    Pedro Contreras; Dianela Osorio; Anjna Devi. Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate. Int. J. Appl. Math. Theor. Phys. 2023, 9(1), 1-13. doi: 10.11648/j.ijamtp.20230901.11

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    AMA Style

    Pedro Contreras, Dianela Osorio, Anjna Devi. Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate. Int J Appl Math Theor Phys. 2023;9(1):1-13. doi: 10.11648/j.ijamtp.20230901.11

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  • @article{10.11648/j.ijamtp.20230901.11,
      author = {Pedro Contreras and Dianela Osorio and Anjna Devi},
      title = {Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {9},
      number = {1},
      pages = {1-13},
      doi = {10.11648/j.ijamtp.20230901.11},
      url = {https://doi.org/10.11648/j.ijamtp.20230901.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20230901.11},
      abstract = {This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first one, represented by a Fermi energy with a value of - 0.4 meV, where the rest of the material parameters, and the degrees of freedom of the normal to the superconducting phase transition are not sensitive to the self-consistent variation of the zero temperature superconducting energy gap. A different case is found when in the self-consistent numerical procedure, the Fermi energy takes a value of - 0.04 meV, indicating that the fermion-dressed quasiparticles have material parameters strongly sensitive to the numerical changes in the zero temperature gap, resulting in a reduced phase space, where the input and output zero superconducting energy values, and the degrees of freedom are separated by the self-consistent numerical analysis. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.},
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate
    AU  - Pedro Contreras
    AU  - Dianela Osorio
    AU  - Anjna Devi
    Y1  - 2023/03/20
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ijamtp.20230901.11
    DO  - 10.11648/j.ijamtp.20230901.11
    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 1
    EP  - 13
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20230901.11
    AB  - This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first one, represented by a Fermi energy with a value of - 0.4 meV, where the rest of the material parameters, and the degrees of freedom of the normal to the superconducting phase transition are not sensitive to the self-consistent variation of the zero temperature superconducting energy gap. A different case is found when in the self-consistent numerical procedure, the Fermi energy takes a value of - 0.04 meV, indicating that the fermion-dressed quasiparticles have material parameters strongly sensitive to the numerical changes in the zero temperature gap, resulting in a reduced phase space, where the input and output zero superconducting energy values, and the degrees of freedom are separated by the self-consistent numerical analysis. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.
    VL  - 9
    IS  - 1
    ER  - 

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Author Information
  • Department of Physics, University of Los Andes, Mérida, Venezuela

  • Department of Brain and Behavioral Sciences, University of Pavia, Pavia, Italy

  • Department of Physics, Himachal Pradesh University, Shimla, India

  • Section