Analog of the Aharonov-Bohm effect in superfluid He/sup 3/-A

Edouard B Sonin

Edouard B Sonin

Claudio Furtado, Alexandre M. de M. Carvalho, L. C. García de Andrade +1 more

In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrate that in the general case the Aharonov-Bohm effect has a contribution both from the rotational and the translational holonomy. We study also Berrys quantum phase for phonons in this systems.

Hananel Davidowitz, Victor Steinberg

We propose a hydrodynamic analog of the Aharonov-Bohm experiment in which second-sound waves are scattered on a quantized vortex in superfluid helium. The time lag that develops between the two sides of a second-sound plane wave impinging on a vortex from the side would be compared. Estimates for these experiments show that for reasonable experimental conditions the wavefront splitting can be readily measured at reduced temperatures of 10 −6 . The advantages of doing this experiment near the superfluid transition is discussed. This experiment would compliment the three other Aharonov-Bohm–type experiments which involve all four possible combinations of classical/quantum waves and classical/quantum vortices. This technique would provide a non-invasive means of investigating the dynamics of quantum vortex nucleation and their stability as well as addressing the problem of multiply quantized.

M. Y. Choi, Minchul Lee

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.