Inhomogeneous Condensates in Planar QED

Abstract
We study the formation of vacuum condensates in $2+1$ dimensional QED in the presence of inhomogeneous background magnetic fields. For a large class of magnetic fields, the condensate is shown to be proportional to the inhomogeneous magnetic field, in the large flux limit. This may be viewed as a {\it local} form of the {\it integrated} degeneracy-flux relation of Aharonov and Casher.

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