  We analyze the influence of classical Gaussian noise on Landau-Zener
transitions during a two-level crossing in a time-dependent regular external
field. Transition probabilities and coherence factors become random due to the
noise. We calculate their two-time correlation functions, which describe the
response of this two-level system to a weak external pulse signal. The spectrum
and intensity of the magnetic response are derived. Although fluctuations are
of the same order of magnitude as averages, the results is obtained in an
analytic form.
