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Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system

  • Stanley A. Bruce ORCID logo EMAIL logo
Published/Copyright: April 1, 2025
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 80 Issue 6

Abstract

In a recent article, we proposed an example suggesting a possible link between the Heisenberg–Euler (HE) model of nonlinear electrodynamics (NLED) and relativistic type-II superconductivity, drawing parallels with the Ginzburg–Landau (GL) theory. In cylindrical coordinates, we considered a concrete static electromagnetic (EM) four-potential in vacuum with Gaussian-like behavior in the radial coordinate. This work extends our analysis to a time-dependent EM potential with a Gaussian-like radial profile and a time-dependent harmonic sinusoidal angular behavior. By deriving nonlinear Maxwell’s equations from the HE Lagrangian, we determine the four-current density. Concurrently, we investigate relativistic type-II superconductivity in analogy with the GL theory. This leads us to propose a specific form for the relativistic vortex’s supercurrent density and to establish a connection between this current and the HE current. As a result, we deduce a relation that allows us to obtain the relativistic order parameter that characterizes the macroscopic quantum state of the superconductor. Thereafter, we present a discussion on possible corrections to our results in relation to the extended GL (EGL) formalism. This formalism provides a more sophisticated description of vortex dynamics in type-II superconductors. Additionally, we briefly comment on high-temperature condensates in intense EM fields where relativistic effects may become prominent. This scenario is particularly relevant to neutron stars, where the formation of superconducting protons and superfluid neutrons in neutron-star outer cores can lead to coupled multiband-like effects.

Keywords: Heisenberg–Euler model; Ginzburg–Landau theory; relativistic superconductivity
Corresponding author: Stanley A. Bruce, Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile, E-mail:

Funding source: Universidad de los Andes, Chile

Award Identifier / Grant number: FAI 12.22

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The author states no conflict of interest.

  6. Research funding: This work was supported by Universidad de Los Andes, Santiago, Chile, through grant FAI 12.22.

  7. Data availability: Not applicable.

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Received: 2024-09-17
Accepted: 2025-02-25
Published Online: 2025-04-01
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2024-0208
Keywords for this article
Heisenberg–Euler model; Ginzburg–Landau theory; relativistic superconductivity

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
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