A model for reducing the angulon operator

TL;DR

This paper introduces a mathematical model for the angulon operator that simplifies spectral analysis by transferring phonon population to a measure-based framework, enabling angular reduction.

Contribution

It presents a novel measure-based formulation of the angulon operator that facilitates angular reduction and spectral analysis.

Findings

Allows angular reduction of the angulon operator

Simplifies spectral analysis of the angulon model

Transfers phonon population to measure without computing it

Abstract

We propose a mathematical model for the recently introduced angulon. In our formulation, the angulon operator is decomposable relative to the field of Hilbert spaces over the probability measure space. That is, we transfer the population of phonons from the inner structure of the many-body Hamiltonian to the definition of the measure. We do not compute the measure itself. However, we demonstrate that the approach allows us to perform angular reduction thereby considerably simplifying the spectral analysis.