Limited regularity of a specific electronic reduced density matrix for molecules

TL;DR

This paper proves that the (N-1)-particle electronic reduced density matrix for molecules with Coulomb interactions is not smooth near certain electronic collisions, highlighting limitations in its regularity.

Contribution

It establishes the limited regularity of the electronic reduced density matrix in molecular systems with Coulomb interactions, a novel theoretical insight.

Findings

The (N-1)-particle reduced density matrix is not smooth near electronic collisions.

Regularity limitations are demonstrated for molecules with Coulomb interactions.

Results apply to non-relativistic molecular Hamiltonians with fixed nuclei.

Abstract

We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we prove that the (N-1)-particle electronic reduced density matrix is not smooth. To appear in Advances in Theoritical and Mathematical Physics.