Two-dimensional Chiral Anomaly in Differential Regularization

The two-dimensional chiral anomaly is calculated using differential regularization. It is shown that the anomaly emerges naturally in the vector and axial Ward identities on the same footing as the four-dimensional case. The vector gauge symmetry can be achieved by an appropriate choice of the mass scales without introducing the seagull term. We have analyzed the reason why such a universal result can be obtained in differential regularization.Comment: 9 pages, RevTex, no figures, a mistake in the massive case pointed out by the referee is correcte

The atmospheric circulation of the super Earth GJ 1214b: Dependence on composition and metallicity

We present three-dimensional atmospheric circulation models of GJ 1214b, a 2.7 Earth-radius, 6.5 Earth-mass super Earth detected by the MEarth survey. Here we explore the planet's circulation as a function of atmospheric metallicity and atmospheric composition, modeling atmospheres with a low mean-molecular weight (i.e., H2-dominated) and a high mean-molecular weight (i.e. water- and CO2-dominated). We find that atmospheres with a low mean-molecular weight have strong day-night temperature variations at pressures above the infrared photosphere that lead to equatorial superrotation. For these atmospheres, the enhancement of atmospheric opacities with increasing metallicity lead to shallower atmospheric heating, larger day-night temperature variations and hence stronger superrotation. In comparison, atmospheres with a high mean-molecular weight have larger day-night and equator-to-pole temperature variations than low mean-molecular weight atmospheres, but differences in opacity structure and energy budget lead to differences in jet structure. The circulation of a water-dominated atmosphere is dominated by equatorial superrotation, while the circulation of a CO2-dominated atmosphere is instead dominated by high-latitude jets. By comparing emergent flux spectra and lightcurves for 50x solar and water-dominated compositions, we show that observations in emission can break the degeneracy in determining the atmospheric composition of GJ 1214b. The variation in opacity with wavelength for the water-dominated atmosphere leads to large phase variations within water bands and small phase variations outside of water bands. The 50x solar atmosphere, however, yields small variations within water bands and large phase variations at other characteristic wavelengths. These observations would be much less sensitive to clouds, condensates, and hazes than transit observations.Comment: 12 pages, 11 figures, 2 tables, accepted to Ap

Enhanced Bishop-Gromov Theorem

The Bishop-Gromov theorem upperbounds the rate of growth of volume of geodesic balls in a space, in terms of the most negative component of the Ricci curvature. In this paper we prove a strengthening of the Bishop-Gromov bound for homogeneous spaces. Unlike the original Bishop-Gromov bound, our enhanced bound depends not only on the most negative component of the Ricci curvature, but on the full spectrum. As a further result, for finite-volume inhomogeneous spaces, we prove an upperbound on the average rate of growth of geodesics, averaged over all starting points; this bound is stronger than the one that follows from the Bishop-Gromov theorem. Our proof makes use of the Raychaudhuri equation, of the fact that geodesic flow conserves phase-space volume, and also of a tool we introduce for studying families of correlated Jacobi equations that we call "coefficient shuffling".Comment: 41 pages, 5 figure

The Smallest Interacting Universe

The co-emergence of locality between the Hamiltonian and initial state of the universe is studied in a simple toy model. We hypothesize a fundamental loss functional for the combined Hamiltonian and quantum state and minimize it by gradient descent. This minimization yields a tensor product structure simultaneously respected by both the Hamiltonian and the state, suggesting that locality can emerge by a process analogous to spontaneous symmetry breaking. We discuss the relevance of this program to the arrow of time problem. In our toy model, we interpret the emergence of a tensor factorization as the appearance of individual degrees of freedom within a previously undifferentiated (raw) Hilbert space. Earlier work [5, 6] looked at the emergence of locality in Hamiltonians only, and found strong numerical confirmation of that raw Hilbert spaces of $\dim = n$ are unstable and prefer to settle on tensor factorization when $n=pq$ is not prime, and in [6] even primes were seen to "factor" after first shedding a small summand, e.g. $7=1+2\cdot 3$. This was found in the context of a rather general potential functional $F$ on the space of metrics $\{g_{ij}\}$ on $\mathfrak{su}(n)$, the Lie algebra of symmetries. This emergence of qunits through operator-level spontaneous symmetry breaking (SSB) may help us understand why the world seems to consist of myriad interacting degrees of freedom. But understanding why the universe has an initial Hamiltonian $H_0$ with a many-body structure is of limited conceptual value unless the initial state, $|\psi_0\rangle$, is also structured by this tensor decomposition. Here we adapt $F$ to become a functional on $\{g,|\psi_0\rangle\}=(\text{metrics})\times (\text{initial states})$, and find SSB now produces a conspiracy between $g$ and $|\psi_0\rangle$, where they simultaneously attain low entropy by settling on the same qubit decomposition

Supersymmetric extensions of k-field models

We investigate the supersymmetric extension of k-field models, in which the scalar field is described by generalized dynamics. We illustrate some results with models that support static solutions with the standard kink or the compact profile.Comment: 11 page

Marine geophysical applications of seasat altimetry and the lithospheric structure of the South Atlantic Ocean

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1987.Microfiche copy available in Archives and Science.Vita.Includes bibliographies.by Adam Paul Freedman.Ph.D

Varying Task Demonstrability to Examine the Roles of Social and Cognitive Factors in Group Transfer Learning

I investigated the importance of cognitive exposure and social interaction for group-to-individual transfer for low-and high-demonstrability tasks. I tested the hypothesis that transfer occurs for high-demonstrability tasks with or without social interaction, but transfer for low-demonstrability tasks only occurs if subjects engage in social interaction. During the transfer phase, subjects either worked in a small group, which permitted social interaction, or viewed a video of a yolked group, which only permitted the transfer of cognitive processes. Analysis of subjects’ pre-post performance difference indicated that transfer is constant regardless of the level of demonstrability. However, overall transfer for the high demonstrability task exceeds transfer of the low demonstrability task

Mud on Your Face, Big Disgrace Vs. The Wisdom of Crowds: Macroforecasters\u27 Herding Behavior Over Time

I examine the herding behavior of macroeconomic forecasters for real GDP growth and unemployment rate forecasts. Although previous research has addressed cross-sectional differences in the propensity to herd, this paper explores changes in herding behavior over time. I present two theories. The first, based on Prospect Theory, predicts that a forecaster’s propensity to herd is inversely related to the size of his recent forecast error. The second theory predicts that the propensity to herd decreases when other forecasters make larger errors. The results reveal significant herding behavior and support for both theories. Implications for consumers of macroforecasts are addressed

Software Processes SAR Motion-Measurement Data

Motion Measurement Processor (MMP) is one of three computer programs that are used together in the operation of a terrain-mapping dual-frequency interferometric synthetic-aperture-radar (SAR) system. The other two programs - Jurassicprok and Calibration Processor - are described in the two immediately preceding articles. MMP acquires all the motion and attitude data collected by onboard instrumentation systems, including radar, laser and camera metrology, inertial navigation systems, and Global Positioning System (GPS) receivers. MMP combines all this information and processes it into all the trajectory information needed to run Jurassicprok, which performs the interferometric processing and mapping functions. MMP includes several Kalman filters for combining and smoothing aircraft motion and attitude data, and least-squares inversion and filtering software tools for solving for interferometric baseline lengths. MMP synchronizes the motion and radar data. It combines the various measurement data into a unified, seven-dimensional reference system and puts out the resulting filtered trajectory and attitude data along with instructions for use of the data by Jurassicprok, as well as the command files used to operate Jurassicprok