Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

Quantum Theory of the Smectic Metal State in Stripe Phases

We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the abscence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases may have already been seen in Nd-doped LSCO.Comment: Brookhaven national Laboratory, University of Illinois at Urbana-Champaign, UCLA and University of Pennsylania; 4 pages, 2 figures, both figures are new. We have corrected the formuals for scaling dimensions (eq. 4) and the discussion that follows from it. The figures have been redrwa

Quasi-1D dynamics and nematic phases in the 2D Emery model

We consider the Emery model of a Cu-O plane of the high temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron-dynamics is strictly one dimensional, and consequently a number of asymptotically exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point- group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.Comment: 8 pages, 5 eps figures; revised manuscript with more detailed discussions; two new figures and three edited figuresedited figures; 14 references; new appendix with a detailed proof of the one-dimensional dynamics of the system in the strong coupling limi

The types of Mott insulator

There are two classes of Mott insulators in nature, distinguished by their responses to weak doping. With increasing chemical potential, Type I Mott insulators undergo a first order phase transition from the undoped to the doped phase. In the presence of long-range Coulomb interactions, this leads to an inhomogeneous state exhibiting ``micro-phase separation.'' In contrast, in Type II Mott insulators charges go in continuously above a critical chemical potential. We show that if the insulating state has a broken symmetry, this increases the likelihood that it will be Type I. There exists a close analogy between these two types of Mott insulators and the familiar Type I and Type II superconductors

Infrared Lightcurves of Near Earth Objects

We present lightcurves and derive periods and amplitudes for a subset of 38 near earth objects (NEOs) observed at 4.5 microns with the IRAC camera on the the Spitzer Space Telescope, many of them having no previously reported rotation periods. This subset was chosen from about 1800 IRAC NEO observations as having obvious periodicity and significant amplitude. For objects where the period observed did not sample the full rotational period, we derived lower limits to these parameters based on sinusoidal fits. Lightcurve durations ranged from 42 to 544 minutes, with derived periods from 16 to 400 minutes. We discuss the effects of lightcurve variations on the thermal modeling used to derive diameters and albedos from Spitzer photometry. We find that both diameters and albedos derived from the lightcurve maxima and minima agree with our previously published results, even for extreme objects, showing the conservative nature of the thermal model uncertainties. We also evaluate the NEO rotation rates, sizes, and their cohesive strengths.Comment: 16 pages, 4 figures, 3 tables, to appear in the Astrophysical Journal Supplement Serie

In Better Fettle: Improvement, Work and Rhetoric in the Transition to Environmental Farming in the North York Moors

Through ethnographic research amongst farmers in the North York Moors, and through broader historical and political analysis, I examine the importance and role of values in hard work and beneficent change in negotiated interactions between policy-makers, farmers and conservationists. Within the context of a shift in agricultural support away from production to environmental protection, and within the context of a local conservation initiative to protect a population of freshwater pearl mussels in the River Esk, I show the importance of these values for the construction of farmers' personhoods and their symbolic relations and means of expression through the landscape. I show how those values are persistent and pervasive, yet at the same time mutable and open to interpretation. In particular, I examine alternative conceptions of beneficent change through recourse to the words fettle and improvement. Fettling places value in long-term, steady and incremental change, whereas improvement places value in changes more closely associated with productivist ideals such as expansion and profit. I suggest that it is the mutability of farming values that gives rise to their persistence as they come to be used and reinterpreted according to the changing contexts of their application and the differing interests of a range of groups and individuals. By showing that farmers are able to uphold and express their values differently I argue that it is not so straightforward to predict farmers' responses to changing political exigencies or local conservation initiatives on the basis of homogenous values or the categorisation of farmers into defined "types". Through a rhetoric-culture approach I argue that changes in farming values through time do not merely reflect changing political interests and farmers' subsequent accommodation of them. Rather, it reflects the continued negotiation of those values between farmers and others in the play of agents and patients in the construction of personhood and the formulation of arguments. I argue that the persistence of fettling interpretations of a value in beneficent change reflects the agentive actions of farmers as it remains a useful argumentative strategy with which they can make indictments against new policy impositions and, moreover, it remains functional in guiding their practices in ways suitable to the environment in which they farm

Liquid Crystal Phases of Quantum Hall Systems

Mean-field calculations for the two dimensional electron gas (2DEG) in a large magnetic field with a partially filled Landau level with index $N\geq 2$ consistently yield ``stripe-ordered'' charge-density wave ground-states, for much the same reason that frustrated phase separation leads to stripe ordered states in doped Mott insulators. We have studied the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase which is stable at $T>0$. Recent measurements of the longitudinal resistivity of a set of quantum Hall devices have revealed that these systems spontaneously develop, at low temepratures, a very large anisotropy. We interpret these experiments as evidence for a stripe nematic phase, and propose a general phase diagram for this system.Comment: 9 pages, 3 figure