Bose-Einstein condensation of strongly correlated electrons and phonons   in cuprate superconductors
  The long-range Froehlich electron-phonon interaction has been identified as the most essential for pairing in high-temperature superconductors owing to poor screening, as is now confirmed by optical, isotope substitution, recent photoemission and some other measurements. I argue that low energy physics in cuprate superconductors is that of superlight small bipolarons, which are real-space hole pairs dressed by phonons in doped charge-transfer Mott insulators. They are itinerant quasiparticles existing in the Bloch states at low temperatures as also confirmed by continuous-time quantum Monte-Carlo algorithm (CTQMC) fully taking into account realistic Coulomb and long-range Froehlich interactions. Here I suggest that a parameter-free evaluation of Tc, unusual upper critical fields, the normal state Nernst effect, diamagnetism, the Hall-Lorenz numbers and giant proximity effects strongly support the three-dimensional (3D) Bose-Einstein condensation of mobile small bipolarons with zero off-diagonal order parameter above the resistive critical temperature Tc at variance with phase fluctuation scenarios of cuprates. 
A.S. Alexandrov