Non-regular Bcs State

In the study of high temperature superconductivity, the pseudogap phenomenon is a widely studied subject. Understanding of it may provide crucial clues for finding the mechanism of high temperature superconductivity. In our proposal, a system governed by the BCS Hamiltonian and coupled to a spin fluctuation is studied. We treat the fluctuation as a noise, which induces a non-unitary evolution. Stationary states in the sense of time-independence and minimum free energy are not canonical ensembles because of the non-unitarity. We find that a gap can lead to energy increase rather than reduction for some quasiparticles. A state in which only a part of quasiparticles are gapped can resolve this dilemma. The transition temperature of the partial gapping is discussed.In the first capture, I review another work that I have done during my graduate study—Triplet exciton in polymeric electroluminescence. Due to self-trapping in polymer, a triplet exciton can be combined with a polaron to form a charged exciton with spin 1/2 or 3/2. The former one is emissive. This combination opens a charged exciton channel to make the triplet exciton emissive, enabling the electroluminescence efficiency to increase from 25 to 50%. A precondition is determined for opening this new channel, namely that the injected current density should exceed a certain threshold which depends on the lifetime of the triplet exciton. In the second capture, I introduce at first a tensor product form of equilibrium states of a non-interaction quasiparticle systems, which can significantly simplify the pseudogap model proposed.