The response of spiral waves to external perturbations in a stable reg
ime of the two-dimensional complex Ginzburg-Landau equation (CGLE) is
investigated. It is shown that the spiral core has a finite mobility a
nd performs Brownian motion when driven by white noise. Combined with
simulation results, this suggests that defect-free and quasifrozen sta
tes in the noiseless CGLE are susceptible to unpaired vortex excitatio
n at any nonzero noise strength.