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Topological Quantum Computing Open Quantum Systems Decoherence

The Aharonov-Casher phase is geometrical and not topological

arXiv

Authors: Igor Kuzmenko, Y. B. Band, Yshai Avishai

Year

2024

Paper ID

37072

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

Abstract

It is demonstrated that the Aharonov-Casher (AC) phase is a geometric phase that, in general, depends on the details of the closed path taken by a particle with a magnetic moment that is subject to an electric field. Consequently, it is not a topological phase. The proof of this statement is obtained by developing a counterexample that elucidates the dependence of the AC phase on the details of the path. Furthermore, we demonstrate that, in the particular example considered here, paths having an Abelian AC phase factor, also have an AC phase that is path-independent, whereas paths having a non-Abelian AC phase factor may have an AC phase that is path-dependent (i.e., not topological).

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This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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It is demonstrated that the Aharonov-Casher (AC) phase is a geometric phase that, in general, depends on the details of the closed path taken by a particle with a magnetic...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2411.04589 [2] arXiv https://arxiv.org/abs/2411.04589 [3] Publisher https://arxiv.org/abs/2411.04589

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