Lie algebra for rotational subsystems of a driven asymmetric top

TL;DR

This paper develops an analytical method to construct the Lie algebra of rotational subsystems in a driven asymmetric top rotor, accounting for degeneracies and using graph representations to handle complex commutators.

Contribution

It introduces a novel inductive approach to generate the Lie algebra for any rotational excitation level in driven asymmetric top molecules.

Findings

Lie algebra constructed for various rotational levels

Graph representation simplifies commutator calculations

Method applicable to complex driven molecular systems

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.