  In the framework of the planar t-J model for cuprates we analyze the
development of a pseudo gap in the density of states, which at low doping
starts to emerge for temperatures T<J and persists up to the optimum doping.
The analysis is based on numerical results for spectral functions obtained with
the finite-temperature Lanczos method for finite two-dimensional clusters.
Numerical results are additionally compared with the self consistent Born
approximation (SCBA) results for hole-like (photoemission) and electron-like
(inverse photoemission) spectra at T=0. The analysis is suggesting that the
origin of the pseudo gap is in short-range antiferromagnetic (AFM) spin
correlations and strong asymmetry between the hole and electron spectra in the
underdoped regime. We analyze also the electron momentum distribution function
(EMD). Our analytical results for a single hole in an AFM based on the SCBA
indicate an anomalous momentum dependence of EMD showing "hole pockets"
coexisting with a signature of an emerging large Fermi surface (FS). The
position of the incipient FS and the structure of the EMD is determined by the
momentum of the ground state. The main observation is the coexistence of two
apparently contradicting FS scenarios. On the one hand, the delta-function like
contributions at (pi/2,pi/2) indicate, that for finite doping a pocket-like
small FS evolves from these points, provided provided that AFM long range order
persists. On the other hand, the discontinuity which appears at the same
momentum is more consistent with with infinitesimally short arc (point) of an
emerging large FS.
