On the Aharonov–Bohm Hamiltonian

César R. de Oliveira, Marciano Pereira

Radha Balakrishnan, Indubala I. Satija

Davide Fermi

Matteo Gallone, Alessandro Michelangeli, Diego Noja

ABSTRACT We characterize the families of self‐adjoint Dirac and Schrödinger operators with Aharonov–Bohm magnetic field, and we exploit the non‐relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short‐scale boundary condition of self‐adjointness. This ensures that the scattering length of the Aharonov–Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac‐AB operators is mapped, in the non‐relativistic limit, into the physically relevant sub‐family of ‐wave, angular‐momentum‐commuting, Schrödinger–AB Hamiltonians with relativistic Dirac approximants.

J.-Q. Liang

K. Bakke

Abstract We study the influence of the Aharonov-Bohm quantum phase on a quantum system described by a non-Hermitian Hamiltonian. We show that a non-Hermitian Hamiltonian has real energy eigenvalues which are influenced by the Aharonov-Bohm quantum phase. In addition, we show that persistent currents can arise. Finally, we calculate the revival times in this two-dimensional system and show that they are influenced by Aharonov-Bohm quantum phase.