  Double layer systems where one layer has electrons and the holes are in a
parallel layer a distance d away are expected to undergo excitonic condensation
at low temperature. This excitonic condensate is traditionally described by a
many-body wavefunction that encodes the coherence between electron and hole
bands. Here we compare the mean-field ground state in the limit of dilute
electron (hole) density with the ground state of a single electron-hole pair in
double-layer system. As the interlayer distance d increases, we find that the
excitonic size, characterized by the width of the momentum-space wavefunction,
also increases. By comparing the single-exciton wavefunction with the
mean-field analysis, we determine the d-dependence of the "diluteness" of the
exciton gas in a balanced double-layer system with given electron (or hole)
density.
