# Expansion of the resolvent in a Feshbach model

## TL;DR

This paper extends previous work on Feshbach resonances by deriving a low-energy expansion of the resolvent for a multichannel Hamiltonian in the resonant case, providing deeper insight into the spectral properties at low energies.

## Contribution

It introduces a low-energy expansion of the resolvent for a multichannel Hamiltonian with Feshbach resonances, building upon prior results and focusing on the resonant case.

## Key findings

- Derived a low-energy expansion of the resolvent $( ext{H}-k^{2})^{-1}$ as $k o 0$ in the resonant case.
- Extended previous results on Feshbach resonances to include the resolvent expansion at low energies.
- Provides mathematical tools for analyzing spectral properties near zero energy in multichannel quantum systems.

## Abstract

In this paper we extend the results proved in (Carlone, R., Correggi, M., Finco, D., Teta, A.: A model for Feshbach Resonances arXiv:1901.08282 [math-ph]) about Feshbach resonances in a multichannel Hamiltonian $\mathcal{H}$, proving a low energy expansion of the resolvent $(\mathcal{H}-k^{2})^{-1}$ as $k\to 0$ in the resonant case.