SLE-type growth processes and the Yang-Lee singularity

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply-connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c=-22/5 and is associated to the Yang-Lee singularity. Our construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version to be publishe

Stationarity of SLE

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.Comment: 14 pages with 1 figur

The mid-infrared spectrum of the transiting exoplanet HD 209458b

We report the spectroscopic detection of mid-infrared emission from the transiting exoplanet HD 209458b. Using archive data taken with the Spitzer/IRS instrument, we have determined the spectrum of HD 209458b between 7.46 and 15.25 microns. We have used two independent methods to determine the planet spectrum, one differential in wavelength and one absolute, and find the results are in good agreement. Over much of this spectral range, the planet spectrum is consistent with featureless thermal emission. Between 7.5 and 8.5 microns, we find evidence for an unidentified spectral feature. If this spectral modulation is due to absorption, it implies that the dayside vertical temperature profile of the planetary atmosphere is not entirely isothermal. Using the IRS data, we have determined the broad-band eclipse depth to be 0.00315 +/- 0.000315, implying significant redistribution of heat from the dayside to the nightside. This work required development of improved methods for Spitzer/IRS data calibration that increase the achievable absolute calibration precision and dynamic range for observations of bright point sources.Comment: 35 pages, 12 figures, revised version accepted by the Astrophysical Journa

Consequences of a Distant Massive Planet on the Large Semi-major Axis Trans-Neptunian Objects

We explore the distant giant planet hypothesis by integrating the large semi-major axis, large pericenter Trans-Neptunian Objects (TNOs) in the presence of the giant planets and an external perturber whose orbit is consistent with the proposed distant, eccentric, and inclined giant planet, so called planet 9. We find that TNOs with semi-major axes greater than 250 au experience some longitude of perihelion shepherding, but that a generic outcome of such evolutions is that the TNOs evolve to larger pericenter orbits, and commonly get raised to retrograde inclinations. This pericenter and inclination evolution requires a massive disk of TNOs (tens of M_\Earth) in order to explain the detection of the known sample today. Some of the highly inclined orbits produced by the examined perturbers will be inside of the orbital parameter space probed by prior surveys, implying a missing signature of the 9th planet scenario. The distant giant planet scenarios explored in this work do not reproduce the observed signal of simultaneous clustering in argument of pericenter, longitude of the ascending node, and longitude of perihelion in the region of the known TNOs

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and some additional improvements. 21 pages, 5 figure