Expansion of the resolvent in a Feshbach model

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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.

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Feshbach Resonances in Ultracold Gases

Eite Tiesinga, Paul Julienne, Rudolf Grimm … (2008)

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.