Emergent physics of rotating quantum impurities in many-body environments

Rotations are found in physics problems at all scales: from spatial motion of celestial bodies, to transitions between quantum states of atoms and molecules. Mathematically, they represent a fundamental class of transformations and symmetries. Unlike spatial displacements, rotational transformations in three-dimensional space are non-commutative: the result of applying a sequence of rotations depends on the order of these operations. This feature makes the emergent physics that involves rotations rather intricate, but instrumental for studies of highly-interconnected many-body systems. In the presence of an environment, rotational properties of an object change, due to the interaction with particles of the environment. Owing to the complexity of this interaction, it can be engineered to exhibit certain properties of interest. In this Thesis, we examine several scenarios of how the rotational behavior of an impurity can be modified by interactions with its environment.