On electromagnetic curves and geometric phase associated with frontals in de-Sitter 2-space

DOĞAN YAZICI B., ÖZKALDI KARAKUŞ S.

Indian Journal of Physics, vol.98, no.3, pp.1021-1030, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 98 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1007/s12648-023-02876-9
  • Journal Name: Indian Journal of Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, INSPEC, zbMATH
  • Page Numbers: pp.1021-1030
  • Keywords: Berry phase, de-Sitter 2-space, Electromagnetic curves, Spacelike frontals, Timelike frontals
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this work, we introduce a Berry phase model which is very important in physics relative to the frontals in de-Sitter 2-space. With this approach, we examine the relationship between a singular curve and Fermi–Walker’s law and Berry’s phase law in de-Sitter 2-space. We give the Rytov curves by using an orthonormal frame of spacelike frontals and timelike frontals with Fermi–Walker parallelism. We express parametric representations of Rytov curves associated with a singular optical fiber. We examine electromagnetic curves associated with orthonormal vectors of spacelike frontals and timelike frontals in de-Sitter 2-space. Hence, we express the magnetic field equations, Lorentz force equations and magnetic trajectory equations along a singular optical fiber. Finally, we give examples that support the theories both physically and geometrically.