Fractal Ohm's law and the Drude model in fractal time

Khalili Golmankhaneh A., Deppman A., Banchuin R., Jørgensen P. E.

Physica B: Condensed Matter, cilt.731, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 731
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.physb.2026.418501
  • Dergi Adı: Physica B: Condensed Matter
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, Compendex, INSPEC
  • Anahtar Kelimeler: Anomalous electrical conduction, Fractal calculus, Fractal Ohm's law, Fractal time, Glassy and disordered materials, Stretched-exponential relaxation
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Classical electrical conduction theories, including Ohm's law and the Drude model, assume charge transport in smooth Euclidean time. However, many disordered and glassy materials exhibit anomalous conduction and relaxation that classical models cannot fully explain. In this work, we present a generalized electrical conduction framework based on fractal calculus, where time evolves on a fractal set with dimension 0<α≤1. Using local fractal derivatives and the associated staircase function, we derive a fractal equation of motion for charge carriers and obtain explicit formulas for drift velocity, current density, and conductivity. The resulting conductivity follows a power-law dependence on the relaxation time, reflecting temporal fractality. The classical Drude result is recovered in the Euclidean limit α=1. The model also produces stretched-exponential relaxation, giving a unified description of steady and transient transport in complex media.