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The effect of an exponentially decaying magnetic field on the dynamics ofDirac fermions in 3+1 dimensions is explored. The spatially decaying magneticfield is assumed to be aligned in the third direction, and is defined by{\mathbf{B}}(x)=B(x){\mathbf{e}}_{z}, with B(x)=B_{0}e^{-\xi\ x/\ell_{B}}.Here, \xi\ is a dimensionless damping factor and \ell_{B}=(eB_{0})^{-1/2} isthe magnetic length. As it turns out, the energy spectrum of fermions in thisinhomogeneous magnetic field can be analytically determined using the Ritusmethod. Assuming the magnetic field to be strong, the chiral condensate and the\textit{local} electric current correlation function are computed in the lowestLandau level (LLL) approximation and the results are compared with thosearising from a strong homogeneous magnetic field. Although the constantmagnetic field B_{0} can be reproduced by taking the limit of \xi-> 0 and/orx-> 0 from B(x), these limits turn out to be singular once the quantumcorrections are taken into account.

Local electric current correlation function in an exponentially decaying magnetic field