Breakdown of Landau Fermi liquid properties in the $2D$ Boson-Fermion model

We study the normal state spectral properties of the fermionic excitations in the Boson-Fermion model. The fermionic single particle excitations show a flattening of the dispersion as the Fermi vector ${\bf k}_{_F}$ is approached from below, forshadowing a Bogoliubov spectrum of a superconducting ground state. The width of the quasiparticle excitations near ${\bf k}_{_F}$ increases monotonically as the temperature is lowered. In the fermionic distribution function this temperature dependence is manifest in a strong modification of $n({\bf k})$ in a small region below ${\bf k}_{_F}$, but a nearly $T$ independant $n({\bf k}_{_F})$.