Eur. Phys. J. B 52, 181-189 (2006)
https://doi.org/10.1140/epjb/e2006-00277-7

The exciton many-body theory extended to any kind of composite bosons

¹ Institut des NanoSciences de Paris, Université Pierre et Marie Curie-Paris 6, Université Denis Diderot-Paris 7, CNRS, UMR 7588, Campus Boucicaut, 140 rue de Lourmel, 75015 Paris, France
² Institute for Experimental Physics, University of Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria

Corresponding author: ^a monique.combescot@insp.jussieu.fr

Received: 12 April 2006
Published online: 7 July 2006

Abstract

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.