Abstract
Interrelation between the two-particle and mean-field problems is used to describe the strong pseudogap and superconducting states in cuprates. We present the strong pseudogap state as an off-diagonal short-range order (ODSRO) originating from quasistationary states of the pair of repulsing particles with large total momentum ($K$ pair). Phase transition from the ODSRO state into the off-diagonal long-range ordered (ODLRO) superconducting state is associated with Bose-Einstein condensation of the $K$ pairs. A checkerboard spatial order observable in the superconducting state in the cuprates is explained by a rise of the $K$-pair density wave. A competition between the ODSRO and ODLRO states leads to the phase diagram typical of the cuprates. Biordered superconducting state of coexisting condensates of Cooper pairs with zero momentum and $K$ pairs explains some properties of the cuprates observed below ${T}_{c}$: Drude optical conductivity, unconventional isotope effect, and two-gap quasiparticle spectrum with essentially different energy scales.
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