  Response theories in condensed matter typically describe the response of an
electron fluid to external electromagnetic fields, while perturbations on
neutral particles are often designed to mimic such fields. Here, we study the
response of fermions to a space-time-dependent velocity field, thereby
sidestepping the issue of a gauge charge. We first develop a semiclassical
chiral kinematic theory that contains a subtle modification of the phase space
measure due to the interplay between the Berry curvature and fluid rotation.
The theory immediately predicts a converse vortical effect, defined as an
orbital magnetization driven by linear velocity. It receives contributions from
magnetic moments on the Fermi surface and Berry curvature of the occupied
bands, with the latter stemming from the modified measure. Then, transcending
semiclassics via a complementary Kubo formalism reveals that the uniform limit
of a clean system receives only the Berry curvature contribution, thus
asserting the importance of the modified measure, while other limits sense the
Fermi surface magnetic moments too. We propose CoSi as a candidate material,
and we suggest conducting magnetometry measurements on a sample under a thermal
gradient to detect the effect. Overall, our study sheds light on the effects of
a space-time-dependent velocity field on electron fluids and paves the way for
exploring quantum materials using new probes and perturbations.
