The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Optical variability of quasars with 20-yr photometric light curves

We study the optical gri photometric variability of a sample of 190 quasars within the SDSS Stripe 82 region that have long-term photometric coverage during ∼1998−2020 with SDSS, PanSTARRS-1, the Dark Energy Survey, and dedicated follow-up monitoring with Blanco 4m/DECam. With on average ∼200 nightly epochs per quasar per filter band, we improve the parameter constraints from a Damped Random Walk (DRW) model fit to the light curves over previous studies with 10–15 yr baselines and ≲ 100 epochs. We find that the average damping time-scale τDRW continues to rise with increased baseline, reaching a median value of ∼750 d (g band) in the rest frame of these quasars using the 20-yr light curves. Some quasars may have gradual, long-term trends in their light curves, suggesting that either the DRW fit requires very long baselines to converge, or that the underlying variability is more complex than a single DRW process for these quasars. Using a subset of quasars with better-constrained τDRW (less than 20 per cent of the baseline), we confirm a weak wavelength dependence of τDRW∝λ0.51 ± 0.20. We further quantify optical variability of these quasars over days to decades time-scales using structure function (SF) and power spectrum density (PSD) analyses. The SF and PSD measurements qualitatively confirm the measured (hundreds of days) damping time-scales from the DRW fits. However, the ensemble PSD is steeper than that of a DRW on time-scales less than ∼ a month for these luminous quasars, and this second break point correlates with the longer DRW damping time-scale

New Perspectives on Substorm Injections

There has been significant progress in understanding substorm injections since the Third International Conference on Substorms in 1996. Progress has come from a combination of new theories, quantitative modeling, and observations--particularly multi-satellite observations. There is now mounting evidence that fast convective flows are the mechanism that directly couples substorm processes in the mid tail, where reconnection occurs, with substorm processes the inner magnetosphere where Pi2 pulsations, auroral breakups, and substorm injections occur. This paper presents evidence that those flows combined with an earthward-propagating compressional wave are responsible for substorm injections and discusses how that model can account for various substorm injection signatures

Explaining the dynamics of the ultra-relativistic third Van Allen radiation belt

Since the discovery of the Van Allen radiation belts over 50 years ago, an explanation for their complete dynamics has remained elusive. Especially challenging is understanding the recently discovered ultra-relativistic third electron radiation belt. Current theory asserts that loss in the heart of the outer belt, essential to the formation of the third belt, must be controlled by high-frequency plasma wave–particle scattering into the atmosphere, via whistler mode chorus, plasmaspheric hiss, or electromagnetic ion cyclotron waves. However, this has failed to accurately reproduce the third belt. Using a data driven, time-dependent specification of ultra-low-frequency (ULF) waves we show for the first time how the third radiation belt is established as a simple, elegant consequence of storm-time extremely fast outward ULF wave transport. High-frequency wave–particle scattering loss into the atmosphere is not needed in this case. When rapid ULF wave transport coupled to a dynamic boundary is accurately specified, the sensitive dynamics controlling the enigmatic ultra-relativistic third radiation belt are naturally explaine