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<p>This work investigates the quantum information metrics—specifically, Shannon information for a two-dimensional relativistic fermionic system with nonminimal coupling to an external electromagnetic field. Starting from a modified Dirac equation derived from a Lorentz-symmetry breaking Lagrangian, we obtain the non-relativistic limit and analyze the resulting effective Schrödinger equation under uniform magnetic fields. The modified Landau quantization reveals energy levels renormalized by the nonminimal coupling parameter <i>g</i>, with eigenfunctions characterized by confluent hypergeometric profiles. We compute the Shannon entropy for the quantized states, demonstrating how <i>g</i> modulates spatial localization and informational uncertainty. The interaction between magnetic field strength and <i>g</i> induces tunable shifts in these information-theoretic quantities, reflecting enhanced or suppressed spin-orbit interactions.</p>

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Probabilistic Analysis of Planar Fermion Systems with Non-minimal Lorentz-violating Couplings

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Allan R. P. Moreira,
  • Abdelmalek Bouzenada,
  • Ridha Horchani,
  • M. Abdi,
  • Faizuddin Ahmed

摘要

This work investigates the quantum information metrics—specifically, Shannon information for a two-dimensional relativistic fermionic system with nonminimal coupling to an external electromagnetic field. Starting from a modified Dirac equation derived from a Lorentz-symmetry breaking Lagrangian, we obtain the non-relativistic limit and analyze the resulting effective Schrödinger equation under uniform magnetic fields. The modified Landau quantization reveals energy levels renormalized by the nonminimal coupling parameter g, with eigenfunctions characterized by confluent hypergeometric profiles. We compute the Shannon entropy for the quantized states, demonstrating how g modulates spatial localization and informational uncertainty. The interaction between magnetic field strength and g induces tunable shifts in these information-theoretic quantities, reflecting enhanced or suppressed spin-orbit interactions.