  The full quantum dynamics of a spinon under external magnetic fields is
investigated by using the time-evolving block decimation (TEBD) method within
the microcanonical picture of transport. We show that the center of the spinon
oscillates back and forth in the absence of dissipation. The quantum many-body
behavior can be understood in a single-particle picture of transport and Bloch
oscillations, where quantum fluctuations induce finite life times. Transport,
oscillations and lifetimes can be tuned to some degree separately by external
fields. Other nontrivial dynamics such as resonance as well as chaos have also
been discussed.
