TT-adic exponential sums of polynomials in one variable

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order

Slow nucleation rates in Chain Inflation with QCD Axions or Monodromy

The previous proposal (by two of us) of chain inflation with the QCD axion is shown to fail. The proposal involved a series of fast tunneling events, yet here it is shown that tunneling is too slow. We calculate the bubble nucleation rates for phase transitions in the thick wall limit, approximating the barrier by a triangle. A similar problem arises in realization of chain inflation in the string landscape that uses series of minima along the monodromy staircase around the conifold point. The basic problem is that the minima of the potential are too far apart to allow rapid enough tunneling in these two models. We entertain the possibility of overcoming this problem by modifying the gravity sector to a Brans-Dicke theory. However, one would need extremely small values for the Brans-Dicke parameter. Many successful alternatives exist, including other "axions" (with mass scales not set by QCD) or potentials with comparable heights and widths that do not suffer from the problem of slow tunneling and provide successful candidates for chain inflation.Comment: 6 pages, 1 figur

Internal Friction of Amorphous Silicon in a Magnetic Field

The internal friction of e-beam amorphous silicon was measured in a magnetic field between 0 and 6 T, from 1.5-20 K, and was found to be independent of the field to better than 8%. It is concluded that the low energy excitations observed in this experiment are predominantly atomic in nature.Comment: 4 pages, 4 figures, REVTe

A Magnetic Dynamo Origin For The Sub-mm Excess In Sgr A*

The sub-mm bump observed in the spectrum of Sgr A* appears to indicate the existence of a compact emitting component within several Schwarzschild radii, $r_S$, of the nucleus at the Galactic Center. This is interesting in view of the predicted circularized flow within $\sim 5-10 r_S$, based on detailed multi-dimensional hydrodynamic simulations of Bondi-Hoyle accretion onto this unusual object. In this paper, we examine the physics of magnetic field generation by a Keplerian dynamo subject to the conditions pertaining to Sgr A*, and show that the sub-mm bump can be produced by thermal synchrotron emission in this inner region. This spectral feature may therefore be taken as indirect evidence for the existence of this circularization. In addition, the self-Comptonization of the sub-mm bump appears to produce an X-ray flux exceeding that due to bremsstrahlung from this region, which may account for the X-ray counterpart to Sgr A* discovered recently by {\it Chandra}. However, the required accretion rate in the Keplerian flow is orders of magnitude smaller than that predicted by the Bondi-Hoyle simulations. We speculate that rapid evaporation, in the form of a wind, may ensue from the heating associated with turbulent mixing of gas elements with large eccentricity as they settle down into a more or less circular (i.e., low eccentricity) trajectory. The spectrum of Sgr A* longward of $\sim 1-2$ mm may be generated outside of the Keplerian flow, where the gas is making a transition from a quasi-spherical infall into a circularized pattern.Comment: 40 pages, 9 figure

Correlations and Renormalization of the Electron-Phonon Coupling in the Honeycomb Hubbard Ladder and Superconductivity in Polyacene

We have performed extensive density matrix renormalization group (DMRG) studies of the Hubbard model on a honeycomb ladder. The band structure (with Hubbard U=0) exhibits an unusual quadratic band touching at half filling, which is associated with a quantum Lifshitz transition from a band insulator to a metal. %SAK as a function of a third-neighbor hopping parameter. For one electron per site, non-zero $U$ drives the system into an insulating state in which there is no pair-binding between added electrons; this implies that superconductivity driven directly by the repulsive electron-electron interactions is unlikely in the regime of small doping, $x\ll 1$. However, the divergent density of states as $x\to 0$, the large values of the phonon frequencies, and an unusual correlation induced enhancement of the electron-phonon coupling imply that lightly doped polyacenes, which approximately realize this structure, are good candidates for high temperature electron-phonon driven superconductivity