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Quantum chaos in Feshbach resonances of the ErYb system

We investigate ultracold magnetic-field-assisted collisions in the so far unexplored ErYb system. The nonsphericity of the Er atom leads to weakly anisotropic interactions that provide the mechanism for Feshbach resonances to emerge. The resonances are moderately sparsely distributed with a density of $0.1\,{\rm G}^{-1}-0.3\,{\rm G}^{-1}$ and exhibit chaotic statistics characterized by a Brody parameter $η\approx 0.5-0.7$. The chaotic behaviour of Feshbach resonances is accompanied by strong mixing of magnetic and rotational quantum numbers in near-threshold bound states. We predict the existence of broad resonances at fields $<300\,{\rm G}$ that may be useful for the precise control of scattering properties and magnetoassociation of ErYb molecules. The high number of bosonic Er-Yb isotopic combinations gives many opportunities for mass scaling of interactions. Uniquely, two isotopic combinations have nearly identical reduced masses (differing by less than $10^{-5}$ relative) that we expect to have strikingly similar Feshbach resonance spectra, which would make it possible to experimentally measure their sensitivity to hypothetical variations of proton-to-electron mass ratio.