Chiral vortical effect and boundary-induced vortical pumping in finite Weyl systems

The chiral vortical effect (CVE) -- an axial current driven by rotation in chiral matter -- appears in systems ranging from relativistic fluids to Weyl semimetals. We present an exact quantum solution of a rotating Weyl fermion in a finite cylinder. We recover the exact current density on the rotation axis obtained by Vilenkin and show that its cross-sectional average vanishes in the thermodynamic limit, establishing that the bulk vortical response is purely a magnetization current. For spin-polarized boundary conditions, we uncover an additional effect beyond the known CVE: a robust family of chiral modes that transport axial charge, $ΔQ=χN^2,Δθ/4π$, under rotation by angle $Δθ$, where $χ$ 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 clarify the quantum structure of the bulk CVE and reveal a boundary-enforced chiral spectral structure underlying vortical response in Weyl systems.