Aharonov–Bohm effect and transmutation of statistics

ABDULLAH VERÇİN, NUSRET GÜÇLÜ

The effects of a standing solenoid in the energy and total angular momentum eigenstates of $N$ anyon moving in a static and uniform magnetic field are investigated. It has been shown that, without changing the statistics of the eigenfunctions, a kind of statistical transmutation in the spectra is possible by adjusting the flux of the solenoid. Keywords: Aharonov-Bohm Effect, Anyons, Transmutation of the Statistics.

Hiroyuki Fukuyama

Mark D. Semon, John R. Taylor

K. Wódkiewicz

An explicit gauge-independent calculation of the bound-state Aharonov-Bohm effect is presented using the hydrodynamic formulation of quantum mechanics. It is pointed out that the Aharonov-Bohm effect is a genuine gauge-independent property of standard quantum mechanics. The statistics of the particle-vortex composites is also briefly mentioned.

Gregory Eskin

Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.

Donald H. Kobe