Pseudogap and Other Precursor Signatures in the Systems with Local Fermion Pairs

We consider precursor effects of the superconducting order which possibly show up in the normal state of high temperature superconducting materials. The local pairs of electrons or holes are formed there well above the transition temperature T$\text{}_{c}$. Due to strong quantum fluctuations the single particle density of states can be partly depleted near the Fermi energy leading to the pseudogap. We claim that this feature should go hand in hand with emergence of the Bogoliubov-type quasiparticles. In the normal state they are expected to be damped and acquire the long lifetime upon passing T$\text{}_{c}$. These Bogoliubov-type quasiparticles may nevertheless become correlated on a finite spatial and temporal scale. We discuss how such short-range pair correlations can be detected experimentally.