The geometry of Hrushovski constructions, I. The uncollapsed case

An intermediate stage in Hrushovski's construction of flat strongly minimal structures in a relational language L produces omega-stable structures of rank omega. We analyze the pregeometries given by forking on the regular type of rank omega in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.Comment: 31 page

On the size of the Fe II emitting region in the AGN Akn 120

We present a reverberation analysis of the strong, variable optical Fe II emission bands in the spectrum of Akn 120, a low-redshift AGN which is one of the best candidates for such a study. On time scales of several years the Fe II line strengths follow the variations in the continuum strength. However, we are unable to measure a clear reverberation lag time for these Fe II lines on any time scale. This is due to the very broad and flat-topped nature of the Fe II cross correlation functions, as compared to the H-beta response which is much more sharply localized in time. Although there is some suggestion in the light curve of a 300-day response time, our statistical analysis does not pick up such a feature. We conclude that the optical Fe II emission does not come from a photoionization-powered region similar in size to the H-beta emitting region, but we cannot say for sure where it does come from. Our results are generally consistent either with emission from a photoionized region several times larger than the H-beta zone, or with emission from gas heated by some other means, perhaps responding only indirectly to the continuum variations.Comment: Accepted for publication in the Ap

Deriving bases for Abelian functions

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.Comment: 35page

Evidence for a ν=5/2\nu=5/2 Fractional Quantum Hall Nematic State in Parallel Magnetic Fields

We report magneto-transport measurements for the fractional quantum Hall state at filling factor $\nu=$ 5/2 as a function of applied parallel magnetic field ($B_{||}$). As $B_{||}$ is increased, the 5/2 state becomes increasingly anisotropic, with the in-plane resistance along the direction of $B_{||}$ becoming more than 30 times larger than in the perpendicular direction. Remarkably, the resistance anisotropy ratio remains constant over a relatively large temperature range, yielding an energy gap which is the same for both directions. Our data are qualitatively consistent with a fractional quantum Hall \textit{nematic} phase

Observation of An Anisotropic Wigner Crystal

We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears near Landau level filling factor $\nu=1/2$ in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component ($B_{||}$) leads to a crossing of the lowest two Landau levels, and an elongated hole wavefunction in the direction of $B_{||}$. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along $B_{||}$ more than 10 times smaller than the resistance perpendicular to $B_{||}$. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal

Anisotropic composite fermions and fractional quantum Hall effect

We study the role of anisotropy on the transport properties of composite fermions near Landau level filling factor $\nu=1/2$ in two-dimensional holes confined to a GaAs quantum well. By applying a parallel magnetic field, we tune the composite fermion Fermi sea anisotropy and monitor the relative change of the transport scattering time at $\nu=1/2$ along the principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the composite fermion Fermi sea. Furthermore, the measured energy gap for the fractional quantum Hall state at $\nu=2/3$ decreases when anisotropy becomes significant. The decrease, however, might partly stem from the charge distribution becoming bilayer-like at very large parallel magnetic fields

Garden of Roses

https://digitalcommons.library.umaine.edu/mmb-ps/2747/thumbnail.jp

Multicomponent fractional quantum Hall states with subband and spin degrees of freedom

In wide GaAs quantum wells where two electric subbands are occupied we apply a parallel magnetic field or increase the electron density to cause a crossing of the two $N=0$ Landau levels of these subbands and with opposite spins. Near the crossing, the fractional quantum Hall states in the filling factor range $1<\nu<3$ exhibit a remarkable sequence of pseudospin polarization transitions resulting from the interplay between the spin and subband degrees of freedom. The field positions of the transitions yield a new and quantitative measure of the composite Fermions' discrete energy level separations. Surprisingly, the separations are smaller when the electrons have higher spin-polarization

Short-Timescale monitoring of the X-ray, UV and broad double-peak emission line of the nucleus of NGC 1097

Recent studies have suggested that the short-timescale ($\lesssim7$ days) variability of the broad ($\sim$10,000 km s$^{-1}$) double-peaked H$\alpha$ profile of the LINER nucleus of NGC1097 could be driven by a variable X-ray emission from a central radiatively inefficient accretion flow (RIAF). To test this scenario, we have monitored the NGC1097 nucleus in X-ray and UV continuum with Swift and the H$\alpha$ flux and profile in the optical spectrum using SOAR and Gemini-South from 2012 August to 2013 February. During the monitoring campaign, the H$\alpha$ flux remained at a very low level --- 3 times lower than the maximum flux observed in previous campaigns and showing only limited ($\sim 20\%$) variability. The X-ray variations were small, only $\sim 13\%$ throughout the campaign, while the UV did not show significant variations. We concluded that the timescale of the H$\alpha$ profile variation is close to the sampling interval of the optical observations, which results in only marginal correlation between the X-ray and H$\alpha$ fluxes. We have caught the AGN in NGC1097 in a very low activity state, in which the ionizing source was very weak and capable of ionizing just the innermost part of the gas in the disk. Nonetheless, the data presented here still support the picture in which the gas that emits the broad double-peaked Balmer lines is illuminated/ionized by a source of high-energy photons which is located interior to the inner radius of the line-emitting part of the disk.Comment: The paper contains 14 pages, 7 figures and is accepted for publication at the Astrophysical Journa