  We consider the single-particle density of states (DOS) in the strongly
correlated double layer (DL) system, without applied external fields. We
demonstrate an unusual collapse effect in the spectrum of the normal
single-particle spectral function at the particular high-symmetry point
corresponding to the specific bunching-point solution of the chemical potential
in the Frenkel channel. We show that at the low-temperature limit the anomalous
spectral function obeys a concave like structure, which is directly related to
the interlayer pair formation and condensation. We calculate the normal DOS
functions, and we find their temperature dependence for different values of the
interlayer Coulomb interaction parameter. We show that the normal electron and
hole DOS functions demonstrate typical condensates double peak structures on
the background of the excitonic pair formation quasiparticle spectra and we
have found the evidence of the hybridization gap in the case of
high-temperature limit, and small interlayer coupling parameter. Meanwhile, we
show a possible crossover from the excitonic condensate regime into the band
insulator state. The structure of the normal DOS spectra, in the Frenkel
channel and for the strong interlayer coupling regime is found gapless for all
temperature limits, which clearly indicates the strong coherence effects in the
DL structure, and the excitonic condensates therein. We have shown that the
excitonic pair formation and pair condensation occurs simultaneously in the DL
system, in contrast with the purely three-dimensional (3D) or two-dimensional
cases (2D), discussed previously.
