Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Afterglows, redshifts, and properties of swift gammaray bursts

We present optical, near-IR, and radio follow-up of 16 Swift bursts, including our discovery of nine afterglows and a redshift determination for three. These observations, supplemented by data from the literature, provide an afterglow recovery rate of 52% in the optical/near-IR, much higher than in previous missions (BeppoSAX, HETE-2, INTEGRAL, and IPN). The optical/near-IR afterglows of Swift events are on average 1.8 mag fainter at t = 12 hr than those of previous missions. The X-ray afterglows are similarly fainter than those of pre-Swift bursts. In the radio the limiting factor is the VLA threshold, and the detection rate for Swift bursts is similar to that for past missions. The redshift distribution of pre-Swift bursts peaked at z similar to 1, whereas the six Swift bursts with measured redshifts are distributed evenly between 0.7 and 3.2. From these results we conclude that ( 1) the pre-Swift distributions were biased in favor of bright events and low-redshift events, ( 2) the higher sensitivity and accurate positions of Swift result in a better representation of the true burst redshift and brightness distributions ( which are higher and dimmer, respectively), and (3) similar to 10% of the bursts are optically dark, as a result of a high redshift and/or dust extinction. We remark that the apparent lack of low-redshift, low-luminosity Swift bursts and the lower event rate than prelaunch estimates ( 90 vs. 150 per year) are the result of a threshold that is similar to that of BATSE. In view of these inferences, afterglow observers may find it advisable to make significant changes in follow-up strategies of Swift events. The faintness of the afterglows means that large telescopes should be employed as soon as the burst is localized. Sensitive observations in RIz and near-IR bands will be needed to discriminate between a typical z similar to 2 burst with modest extinction and a high-redshift event. Radio observations will be profitable for a small fraction (similar to 10%) of events. Finally, we suggest that a search for bright host galaxies in untriggered BAT localizations may increase the chance of finding nearby low-luminosity GRBs.