  We present a theoretical study of spin-3/2 hole transport through mesoscopic
rings, based on the spherical Luttinger model. The quasi-one-dimensional ring
is created in a symmetric two-dimensional quantum well by a singular-oscillator
potential for the radial in-plane coordinate. The quantum-interference
contribution to the two-terminal ring conductance exhibits an energy-dependent
Aharonov-Anandan phase, even though Rashba and Dresselhaus spin splittings are
absent. Instead, confinement-induced heavy-hole - light-hole mixing is found to
be the origin of this phase, which has ramifications for magneto-transport
measurements in gated hole rings.
