  Recently, transformation from random to chaotic behavior in the statistics of
Fano-Feshbach resonances was observed in thulium atoms with rising ensemble
temperature. We performed random matrix theory simulations of such spectra and
analyzed the resulting statistics. Our simulations show that, when evaluated in
terms of the Brody parameter, resonance statistics do not change or change
insignificantly with rising temperature if temperature is the only changing
parameter. In the experiments evaluated, temperature was changed simultaneously
with optical dipole trap depth. Thus, simulations included the Stark shift
based on the known polarizability of the free atoms and assuming their
polarizability remains the same in the bound state. Somewhat surprisingly, we
found that, while including the Stark shift does lead to minor statistical
changes, it does not change the resonance statistics and, therefore, is not
responsible for the experimentally observed statistic transformation. This
observation suggests that either our assumption regarding the polarizability of
Feshbach molecules is poor or that an additional mechanism changes the
statistics and leads to more chaotic statistical behavior.
