Direct integral description of angulon

TL;DR

This paper introduces a new mathematical representation of the angulon, enabling the derivation of a system of equations for its eigenspaces and providing spectral estimates, with implications for phonon contributions in superfluid helium.

Contribution

It presents a decomposable operator representation of the angulon, leading to a finite system of equations for eigenspaces and spectral bounds, extending understanding of phonon effects.

Findings

The representation allows explicit eigenspace solutions for finite phonon numbers.

The spectral infimum can be estimated using the derived equations.

Two-phonon excitations significantly affect molecular energy in superfluid helium.

Abstract

We propose a representation of angulon in which the angulon operator is decomposable relative to the field of Hilbert spaces over the probability measure space, and the probability measure corresponds to the total-number operator of phonons. In this representation we are able to find the system of $N+1$ equations whose solutions form the eigenspace of the angulon operator, where $1\leq N<\infty$ is the number of phonon excitations. Using this result we estimate the infimum of the spectrum. In the special case $N=1$, the lowest energy approximates to the value which is already known in the literature. Our findings indicate that two-phonon excitations ($N=2$) contribute notably to the energy of a molecule in superfluid $^4$He.