  We investigate the spectral and dynamical properties of a quantum particle
constrained on a ring threaded by a magnetic flux in presence of a complex
(non-Hermitian) potential. For a static magnetic flux, the quantum states of
the particle on the ring can be mapped into the Bloch states of a complex
crystal, and magnetic flux tuning enables to probe the spectral features of the
complex crystal, including the appearance of exceptional points. For a
time-varying (linearly-ramped) magnetic flux, Zener tunneling among energy
states is realized owing to the induced electromotive force. As compared to the
Hermitian case, striking effects are observed in the non-Hermitian case, such
as a highly asymmetric behavior of particle motion when reversing the direction
of the magnetic flux and field-induced delayed transparency.
