Lie algebra for rotational subsystems of a driven asymmetric top
Abstract
We present an analytical approach to construct the Lie algebra of
finite-dimensional subsystems of the driven asymmetric top rotor.
Each rotational level is degenerate due to the isotropy of space, and
the degeneracy increases with rotational excitation. For a given rotational
excitation, we determine the nested commutators between drift and drive
Hamiltonians using a graph representation. We then generate the
Lie algebra for subsystems with arbitrary rotational excitation using an
inductive argument.