A pairing Hamiltonian H(Γ) with a non-separable interaction kernel Γ produces HTS for relatively weak interactions. The doping and temperature dependence of Γ(x,T) and the chemical potential μ(x) is determined by a probabilistic filling of the electronic states in the cuprate unit cell. A diverse set of HTS and normal state properties is examined, including the SC phase transition boundary TC(x), SC gap Δ(x,T), entropy S(x,T), specific heat C(x,T), and spin susceptibility χs(x,T). Detailed x,T agreement with cuprate experiment is obtained for all properties. © 2014 Elsevier B.V. All rights reserved.

A pairing Hamiltonian H(Γ) with an interaction kernel Γ characterized by [-^Γ0,-^α0], where ^Γ0 denotes the separable part and ^α0 the degree of non-separability, produces high temperature superconductivity for both attractive ^Γ0>0 and repulsive ^Γ0<0 when ^α0>0. For ^Γ0>0, typical HTS properties, e.g. cuprate, are produced. Repulsive ^Γ0<0 produces a distinct difference in the kinetic energy dependence of the SC gap, significantly altering thermodynamic properties.

Quasi-periodic eruptions (QPEs) are luminous bursts of soft X-rays from the nuclei of galaxies, repeating on timescales of hours to weeks1-5. The mechanism behind these rare systems is uncertain, but most theories involve accretion disks around supermassive black holes (SMBHs) undergoing instabilities6-8 or interacting with a stellar object in a close orbit9-11. It has been suggested that this disk could be created when the SMBH disrupts a passing star8,11, implying that many QPEs should be preceded by observable tidal disruption events (TDEs). Two known QPE sources show long-term decays in quiescent luminosity consistent with TDEs4,12 and two observed TDEs have exhibited X-ray flares consistent with individual eruptions13,14. TDEs and QPEs also occur preferentially in similar galaxies15. However, no confirmed repeating QPEs have been associated with a spectroscopically confirmed TDE or an optical TDE observed at peak brightness. Here we report the detection of nine X-ray QPEs with a mean recurrence time of approximately 48 h from AT2019qiz, a nearby and extensively studied optically selected TDE16. We detect and model the X-ray, ultraviolet (UV) and optical emission from the accretion disk and show that an orbiting body colliding with this disk provides a plausible explanation for the QPEs.