Exponential decay of eigenfunctions of Brown-Ravenhall operators

TL;DR

This paper proves that eigenfunctions of certain quantum operators decay exponentially, under specific symmetry and spectral conditions, enhancing understanding of their spatial behavior.

Contribution

It establishes the exponential decay of eigenfunctions for reductions of Brown-Ravenhall operators across various symmetry representations, under spectral assumptions.

Findings

Eigenfunctions decay exponentially under specified conditions

Decay holds for all irreducible representations considered

Results apply to operators with eigenvalues below the essential spectrum

Abstract

We prove the exponential decay of eigenfunctions of reductions of Brown-Ravenhall operators to arbitrary irreducible representations of rotation-reflection and permutation symmetry groups under the assumption that the corresponding eigenvalues are below the essential spectrum.