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On the alleged nonlocal and topological nature of the molecular Aharonov-Bohm effect

Erik Sjöqvist

Published Oct 31, 2003• 3 citations
OpenAlex

Abstract

The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\\otimes \\epsilon$ Jahn-Teller system is shown to be essentially analogues to an anisotropic Aharonov-Casher effect for an electrically neutral spin$-{1/2}$ particle encircling a certain configuration of lines of charge.

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arXiv:quant-ph/0310032•Journal of Physics A Mathematical and General•Jan 6, 2004•4 citations
The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic EotimesepsilonE\\otimes \\epsilonEotimesepsilon Jahn-Teller system is shown to be essentially analogues to an anisotropic Aharonov-Casher effect for an electrically neutral spin−1/2-{1/2}−1/2 particle encircling a certain configuration of lines of charge.
The Aharonov-Bohm effect is one of the most comprehensible examples of quantum non-locality. The so called molecular Aharonov-Bohm effect displays great similarities with the latter, but still, we show how this effect can be explained using arguments relying solely on locality, whereby we mean that the effect can be traced down to a force acting locally on the phase space distribution. Our method hinges on studying the system in its momentum representation, and introducing a conjugate gauge which render an everywhere non-zero synthetic magnetic field. The resulting Lorenz force induces a transverse current which can be attributed the equivalence of an intrinsic spin Hall effect. The idea is demonstrated for the linear Exe Jahn-Teller model and applied to the Li3 molecule, for which its corresponding Hamiltonian is obtained by diabatization of ab intio determined adiabatic potential energy surfaces.
Abstract The Aharonov–Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this paper, we study a variant of the AB effect that apparently challenges this concept. The significance of weak values and nonlocal equations of motion is discussed as part of the analysis, shedding light on and connecting all these fundamental concepts.
We establish systematic consolidation of the Aharonov–Bohm (AB) and Aharonov–Casher effects including their scalar counterparts. Their formal correspondences in acquiring topological phases are revealed on the basis of the gauge symmetry in non-simply-connected spaces and the adiabatic condition for the state of magnetic dipoles. In addition, investigation of basic two-body interactions between an electric charge and a magnetic dipole clarifies their appropriate relative motions and discloses physical interrelations between the effects. Based on the two-body interaction, we also construct an exact microscopic description of the AB effect, where all the elements are treated on equal footing, i.e., magnetic dipoles are described quantum-mechanically and electromagnetic fields are quantized. This microscopic analysis not only confirms the conventional (semiclassical) results and the topological nature but also allows one to explore the fluctuation effects due to the precession of the magnetic dipoles with the adiabatic condition relaxed.