Inadequacy of hydrodynamical theories of the Aharonov-Bohm effect

J.-Q. Liang, X. X. Ding

Heinz J. Rothe

Georgi Gary Rozenman, Kyle I. McKee, Arnaud Lazarus +2 more

We report the results of an experimental study of an analog of the Aharonov-Bohm (AB) effect achieved with the hydrodynamic pilot-wave system. A walking droplet is confined to an annular cavity that encircles a shielded vortex, but lies outside its range of direct influence. While there is no vortex-induced flow in the immediate vicinity of the droplets, the vortex modifies the droplet's spatially extended pilot-wave field that guides its motion, producing a vortex-dependent bias in the droplet's orbital speed. High-speed tracking and delay-embedding reconstructions yield Wigner-like phase-space distributions for this hydrodynamic system that exhibits a rigid, flux-dependent translation, providing a force-free, gauge-like realization of an AB-type phase.

Vladimir D. Skarzhinsky

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.

P. Bocchieri, A. Loinger