  A gas of interacting particles is a paradigmatic example of chaotic systems.
It is shown here that even if all but one particle are fixed in generic
positions, the excited states of the moving particle are chaotic. They are
characterized by the number of principal components (NPC) -- the number of
integrable system eigenstates involved into the non-integrable one, which
increases linearly with the number of strong scatterers. This rule is a
particular case of the general effect of an additional perturbation on the
system chaotic properties. The perturbation independence criteria supposing the
system chaoticity increase are derived here as well. The effect can be observed
in experiments with photons or cold atoms as the decay of observable
fluctuation variance, which is inversely proportional to NPC, and, therefore,
to the number of scatterers. This decay indicates that the eigenstate
thermalization is approached. The results are confirmed by numerical
calculations for a harmonic waveguide with zero-range scatterers along its
axis.
