Aharonov-Bohm rings in de Sitter expanding universe

Abstract

The $(1+3)$-dimensional Dirac equation of the fermions moving in ideal Aharonov-Bohm rings in the de Sitter expanding universe is used for deriving the exact expressions of the general relativistic partial currents and corresponding energies. In the de Sitter geometry, these quantities depend on time but these are related each other just as in the non-relativistic case or in special relativity. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. The total relativistic persistent current at $T=0$ takes over this property even though it is evolving in time because of the de Sitter expansion.

17 pages, 2 figures, some typos corrected

References in corpus (5)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional Integer Quantum Hall effect in graphene
• Spin states and persistent currents in mesoscopic rings: spin-orbit interactions
• The physical meaning of the de Sitter invariants
• Transport, Aharonov-Bohm, and Topological Effects in Graphene Molecular Junctions and Graphene Nanorings