Aharonov-Bohm effect revisited

Abstract

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 effect such as 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.

arXiv commentThis article is an expended version of arXiv:1007.3979. Note the change of the title

References in corpus (12)

• A new approach to hyperbolic inverse problems
• High-Velocity Estimates for the Scattering Operator and Aharonov-Bohm Effect in Three Dimensions
• The Aharonov-Bohm Effect and Tonomura et al. Experiments. Rigorous Results
• A new approach to hyperbolic inverse problems II (Global step)
• Aharonov-Bohm Effect and High-Velocity Estimates of Solutions to the Schrödinger Equation
• The Electric Aharonov-Bohm Effect
• Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach
• Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect
• Inverse boundary value problems for systems of partial differential equations
• A Simple Proof of Magnetic and Electric Aharonov-Bohm Effects
• The Aharonov-Bohm effect in spectral asymptotics of the magnetic Schrödinger operator
• Combined Electric and Magnetic Aharonov-Bohm Effects