How composite bosons really interact

TL;DR

This paper clarifies the differences in interactions between composite and elementary bosons, emphasizing overlooked physical processes and extending the theory to non-eigenstate fermion pairs relevant in quantum information.

Contribution

It provides a detailed conceptual analysis of composite boson interactions and extends existing many-body theory to non-eigenstate fermion pairs.

Findings

Distinction between composite and elementary boson interactions clarified

Extension of Coulomb and Pauli scatterings to non-eigenstate fermion pairs

Insights applicable beyond semiconductor physics, including quantum information

Abstract

The aim of this paper is to clarify the conceptual difference which exists between the interactions of composite bosons and the interactions of elementary bosons. A special focus is made on the physical processes which are missed when composite bosons are replaced by elementary bosons. Although what is here said directly applies to excitons, it is also valid for bosons in other fields than semiconductor physics. We in particular explain how the two basic scatterings -- Coulomb and Pauli -- of our many-body theory for composite excitons can be extended to a pair of fermions which is not an Hamiltonian eigenstate -- as for example a pair of trapped electrons, of current interest in quantum information.