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Recently, transformation from random to chaotic behavior in the statistics ofFano-Feshbach resonances was observed in thulium atoms with rising ensembletemperature. We performed random matrix theory simulations of such spectra andanalyzed the resulting statistics. Our simulations show that, when evaluated interms of the Brody parameter, resonance statistics do not change or changeinsignificantly with rising temperature if temperature is the only changingparameter. In the experiments evaluated, temperature was changed simultaneouslywith optical dipole trap depth. Thus, simulations included the Stark shiftbased on the known polarizability of the free atoms and assuming theirpolarizability remains the same in the bound state. Somewhat surprisingly, wefound that, while including the Stark shift does lead to minor statisticalchanges, it does not change the resonance statistics and, therefore, is notresponsible for the experimentally observed statistic transformation. Thisobservation suggests that either our assumption regarding the polarizability ofFeshbach molecules is poor or that an additional mechanism changes thestatistics and leads to more chaotic statistical behavior.

Random matrix theory analysis of a temperature-related transformation in statistics of Fano-Feshbach resonances in Thulium atoms