Quantum structure of the chiral vortical effect and boundary-induced vortical pumping

The chiral vortical effect (CVE) -- an axial current driven by rotation in chiral matter -- appears in systems ranging from relativistic fluids to Weyl semimetals, yet its quantum origin remains unclear because existing derivations are semiclassical. We present an exact quantum solution of a rotating Weyl fermion in a finite cylinder. We show that the bulk vortical response is entirely a magnetization current while the current density on the rotation axis remains finite and matches semiclassical predictions. For spin-polarized boundary conditions, we uncover an additional effect beyond the known CVE: a robust family of chiral modes that transport axial charge, $\Delta Q=\chi N^2\,\Delta\theta/4\pi$, under rotation by angle $\Delta\theta$, where $\chi$ is the Weyl node chirality and $N$ is the number of chiral modes. The pump is independent of temperature, Fermi level and Weyl velocities, but depends on the UV-sensitive number $N$. These results establish a fully quantum picture of the CVE and reveal a boundary-enforced chiral spectral structure underlying vortical response in Weyl systems.