% $Id: hennebabs.tex,v 0.1 2002/06/19 08:20:02 tim Exp tim $

\documentclass[12pt]{article}
\addtolength{\textwidth}{2cm}
\addtolength{\textheight}{4cm}
\addtolength{\headsep}{-2cm}
\addtolength{\oddsidemargin}{-1cm}

\begin{document}
\thispagestyle{empty}
\pagestyle{empty}

{\large
\centerline{\bf Excitons in Semiconductors:}
\centerline{\bf Phase Space Shrinkage and Dissociation vs.\ High Population}}

\ 

\centerline{\underline{K. Henneberger}, T. Schmielau}

\centerline{\em Universit\"at Rostock, Fachbereich Physik,
                18051 Rostock, Germany}

\ 

\noindent

High population of excitons intuitively suggests the possibility of
Bose-Einstein-Condensation (BEC), partial ionization (Mott transition),
and of optical gain and with it lasing.
However, any serious approach to all these problems has to consider
the internal structure of excitons, actually being correlated composites of
fermions, whereas a simple discrimination between bound and unbound pairs
bears some arbitrariness.
In a unique Green's functions (GF) approach, this internal structure is
described by T-matrix diagrams, which need to be considered on equal footing
in the one- and two-particle GF.
This is because, on the one hand, the chemical potential (CP) is (exclusively)
determined by the one-particle GF and no alternative definition, e.g.\ with
the two-particle GF is possible. On the other hand, the CP
through the Kubo-Martin-Schwinger condition for the two-particle GF fixes the
crossover from absorption to gain and, hence, the frequency region available
for lasing. Excitonic lasing would then require the CP to approach the exciton
energy, so that a significant part of the excitonic absorption peak turns
into gain. The very same condition, however, also determines the occurance 
of Bose-Einstein-Condensation.
Moreover, on closer inspection both effects are connected with the finite
size of the sample: BEC is defined as a ground state population that is
proportional to the size of the sample, while lasing requires the gain
to compensate for the round trip loss.

Using a quantum kinetic approach to semiconductor light emission [1]
combined with numerical results for the ladder approximation to the T-matrix
for an extensive region of parameters [2], we present phase diagrams and
laser spectra on this basis, i.e.\ neglecting various other effects like
inhomogeneous broadening and damping through phonons and photons,
and discuss the relation between the two effects of BEC
and lasing in semiconductors.
\\[1cm]
[1] Phys.~Rev.~Lett.~{\bf 76}, 1820 (1996)\\\relax
[2] Tim Schmielau, Thesis, Univ.~Rostock (2001)
\end{document}
