  We develop a theory of orbital pumping, which corresponds to the emission of
orbital currents from orbital dynamics. This phenomenon exhibits two distinct
characteristics compared to spin pumping. Firstly, while spin pumping generates
solely spin (angular momentum) currents, orbital pumping yields both orbital
angular momentum currents and orbital angular position currents. Secondly,
lattice vibrations induce orbital dynamics and associated orbital pumping as
the orbital angular position is directly coupled to the lattice. These pumped
orbital currents can be detected as transverse electric voltages via the
inverse orbital(-torsion) Hall effect, stemming from orbital textures. Our work
proposes a new avenue for generating orbital currents and provides a broader
understanding of angular momentum dynamics encompassing spin, orbital, and
phonon.
