Aharonov–Casher effect

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The Aharonov–Casher effect is a quantum mechanical phenomenon in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It is used for example to observe interference of neutrons or fluxons.

In both effects the particle acquires some phase shift (\varphi) while traveling along some path P. In the Aharonov–Bohm effect it is

\varphi_{AB} = \frac{q}{\hbar} \int_P \mathbf{A} \cdot d\mathbf{x}

While for the Aharonov–Casher effect it is

\varphi_{AC} = \frac{1}{\hbar c^2} \int_P (\mathbf{E}\times \boldsymbol \mu) \cdot d\mathbf{x}

where q is its charge and \boldsymbol \mu is the magnetic moment.

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