  Off-central heavy-ion collisions are known to feature magnetic fields with
magnitudes and characteristic gradients corresponding to the scale of the
strong interactions. In this work, we employ equilibrium lattice simulations of
the underlying theory, QCD, involving similar inhomogeneous magnetic field
profiles to achieve a better understanding of this system. We simulate three
flavors of dynamical staggered quarks with physical masses at a range of
magnetic fields and temperatures, and extrapolate the results to the continuum
limit. Analyzing the impact of the field on the quark condensate and the
Polyakov loop, we find non-trivial spatial features that render the QCD medium
qualitatively different as in the homogeneous setup, especially at temperatures
around the transition. In addition, we construct leading-order chiral
perturbation theory for the inhomogeneous background and compare its prediction
to our lattice results at low temperature. Our findings will be useful to
benchmark effective theories and low-energy models of QCD for a better
description of peripheral heavy-ion collisions.
