Tunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime

Recently, Dial et al. presented measurements of the tunneling density of states into the bulk of a two dimensional electron gas under strong magnetic fields. Several high energy features appear in the measured spectrum showing a distinct dependence on filling factor and a unique response to temperature. We present a quantitative account of the observed structure, and argue it results from the repulsive Coulomb interactions between the tunneling electron and states localized at disorder potential wells. The quenching of the kinetic energy by the applied magnetic field leads to an electron addition spectrum that is primarily determined by the external magnetic field and is nearly independent of the disorder potential. Using a Hartree-Fock model we reproduce the salient features of the observed structure

Least squares approximations of measures via geometric condition numbers

For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine subspace. Such approximations are given by averaging real-valued multivariate functions which are typically scalings of squared (d+1)-volumes of (d+1)-simplices. Specifically, we show that such averages are comparable to the square of the d-dimensional least squares error of that measure, where the comparison depends on a simple quantitative geometric property of it. This result is a higher dimensional generalization of the elementary fact that the double integral of the squared distances between points is proportional to the variance of measure. We relate our work to two recent algorithms, one for clustering affine subspaces and the other for Monte-Carlo SVD based on volume sampling

A Universe Without Weak Interactions

A universe without weak interactions is constructed that undergoes big-bang nucleosynthesis, matter domination, structure formation, and star formation. The stars in this universe are able to burn for billions of years, synthesize elements up to iron, and undergo supernova explosions, dispersing heavy elements into the interstellar medium. These definitive claims are supported by a detailed analysis where this hypothetical "Weakless Universe" is matched to our Universe by simultaneously adjusting Standard Model and cosmological parameters. For instance, chemistry and nuclear physics are essentially unchanged. The apparent habitability of the Weakless Universe suggests that the anthropic principle does not determine the scale of electroweak breaking, or even require that it be smaller than the Planck scale, so long as technically natural parameters may be suitably adjusted. Whether the multi-parameter adjustment is realized or probable is dependent on the ultraviolet completion, such as the string landscape. Considering a similar analysis for the cosmological constant, however, we argue that no adjustments of other parameters are able to allow the cosmological constant to raise up even remotely close to the Planck scale while obtaining macroscopic structure. The fine-tuning problems associated with the electroweak breaking scale and the cosmological constant therefore appear to be qualitatively different from the perspective of obtaining a habitable universe.Comment: 27 pages; 4 figure

Collider Signals of Top Quark Flavor Violation from a Warped Extra Dimension

We study top quark flavor violation in the framework of a warped extra dimension with the Standard Model (SM) fields propagating in the bulk. Such a scenario provides solutions to both the Planck-weak hierarchy problem and the flavor puzzle of the SM without inducing a flavor problem. We find that, generically, tcZ couplings receive a huge enhancement, in particular the right handed ones can be O(1%). This results in BR(t -> c Z) at or above the sensitivity of the Large Hadron Collider (LHC). At the International Linear Collider (ILC), single top production, via e^+ e^- -> t \bar c, can be a striking signal for this scenario. In particular, it represents a physics topic of critical importance that can be explored even with a relatively low energy option, close to the tc threshold. At both the LHC and the ILC, angular distributions can probe the above prediction of dominance of right-handed couplings.Comment: 5 pages, references added, comment added regarding models with custodial symmetry for Z -> b \bar