Global Spectral Gap in Bosonic Molecular Hamiltonians

TL;DR

This paper proves the existence of a uniform spectral gap in bosonic molecular Hamiltonians, indicating stability and energy separation, by employing the Feshbach-Schur map technique.

Contribution

It introduces a novel application of the Feshbach-Schur map to establish a global spectral gap in bosonic molecular Hamiltonians, improving upon prior methods.

Findings

Existence of a uniform spectral gap proven

Application of Feshbach-Schur map to molecular Hamiltonians

Enhanced understanding of molecular stability

Abstract

We consider a neutral bosonic molecule in the Born-Oppenheimer approximation without spin and assume the physically obvious assertion that a neutral molecule prefers to break into smaller neutral clusters. We prove the existence of a global in space/uniform spectral gap between the ground state and first excited state energies. To do so, we improve upon previous results using a different tool, the time-independent Feshbach-Schur map.