Attaining external field control of bimolecular chemical reactions has long been a coveted goal of physics and chemistry. Using coupled-channel statistical theory, we explore how hyperfine interactions and magnetic fields can be used to control the chemical reaction Li + CaH -> LiH + Ca at ultralow temperatures. We observe large field effects on the reaction cross sections, opening up the possibility of controlling ultracold barrierless chemical reactions by tuning selected hyperfine states of the reactants with an external magnetic field . In the second part of this talk, I will address the problem of describing angular momentum dynamics in quantum many-body systems, which represents a seemingly impossible task requiring addition of an essentially infinite number of quantum angular momenta. We develop a numerically exact diagrammatic Monte Carlo approach to angular momentum properties of quantum many-body systems possessing a macrosopic number of degrees of freedom, which merges the usual Feynman diagrams with the angular momentum diagrams of atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. To exemplify the capabilities of the approach, we apply it to the angulon problem?an extended impurity (e.g., a molecule) whose rotation is coupled to collective excitations of bosons .
 T. V. Tscherbul and J. Klos, Magnetic tuning of ultracold barrierless chemical reactions, arXiv:1904.12119.
 G. Bighin, T. V. Tscherbul, and M. Lemeshko, Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems, Phys. Rev. Lett. 121, 165301 (2018).