  We show that Aharonov-Bohm (AB) oscillations in the magnetic moment of an
integrable ballistic quantum dot can be destroyed by a time dependent magnetic
flux. The effect is due to a nonequilibrium population of perfectly coherent
electronic states. For real ballistic systems the equilibrization process,
which involves a special type of inelastic electron backscattering, can be so
ineffective, that AB oscillations are suppressed when the flux varies with
frequency $\omega\sim$ 10$^7$-10$^8$ s$^{-1}$. The effect can be used to
measure relaxation times for inelastic backscattering.
