Thermodynamics and tunneling spectroscopy in the pseudogap regime of the boson fermion model

Motivated by the STM experimental data on Bi_2 Sr_2 CaCU_2 O_{8+x} which indicate the tunneling conductance asymmetry sigma(-V) not equal sigma(V), we report that such a behavior can be explained in terms of the boson fermion model. It has been shown in the recent studies, based on various selfconsistent techniques to capture the many-body effects, that the low energy spectrum of the boson fermion model is featured by an appearance of the pseudogap at T^* > T_c. We argue that the pseudogap structure has to exhibit a particle-hole asymmetry. This asymmetry may eventually depend on the boson concentration.