Deformations of colored sl(N) link homologies via foams

We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher representation theoretic structures and generalizing the Karoubi envelope approach of Bar-Natan and Morrison we explicitly compute the deformed invariants in terms of undeformed type A link homologies of lower rank and color.Comment: 64 pages, many figure

Coherent description of the intrinsic and extrinsic anomalous Hall effect in disordered alloys on an abab initioinitio level

A coherent description of the anomalous Hall effect (AHE) is presented that is applicable to pure as well as disordered alloy systems by treating all sources of the AHE on equal footing. This is achieved by an implementation of the Kubo-St\v{r}eda equation using the fully relativistic Korringa-Kohn-Rostoker (KKR) Green's function method in combination with the Coherent Potential Approximation (CPA) alloy theory. Applications to the pure elemental ferromagnets bcc-Fe and fcc-Ni led to results in full accordance with previous work. For the alloy systems fcc-Fe$_x$Pd$_{1-x}$ and fcc-Ni$_x$Pd$_{1-x}$ very satisfying agreement with experiment could be achieved for the anomalous Hall conductivity (AHC) over the whole range of concentration. To interpret these results an extension of the definition for the intrinsic AHC is suggested. Plotting the corresponding extrinsic AHC versus the longitudinal conductivity a linear relation is found in the dilute regimes, that allows a detailed discussion of the role of the skew and side-jump scattering processes.Comment: * shortened manuscript * slight rewordings * changed line style in Fig 1 * corrected misprinted S (skewness) factor * merged Fig. 3 with Fig. 1 * new citation introduce

Critical Charges on Strange Quark Nuggets and Other Extended Objects

We investigate the behavior of the critical charge for spontaneous pair production, $Z_C$, defined as the charge at which the total energy of a $K$-shell electron is $E=-m_e$, as a function of the radius $R$ of the charge distribution. Our approach is to solve the Dirac equation for a potential $V(r)$ consisting of a spherically symmetrical charge distribution of radius $R$ and a Coulomb tail. For a spherical shell distribution of the type usually associated with color-flavor locked strange quark nuggets, we confirm the relation $Z_C=0.71 R({\rm fm})$ for sufficiently large $R$ obtained by Madsen, who used an approach based on the Thomas-Fermi model. We also present results for a uniformly charged sphere and again find that $Z_C\sim R$ for large enough $R$. Also discussed is the behavior of $Z_C$ when simple {\it ad hoc} modifications are made to the potential for $0\leq r < R$.Comment: 7 pages, 6 figure

Langmuir wave self-focusing versus decay instability

Electron trapping in a finite amplitude Langmuir wave (LW) leads to a frequency shift, \Delta\omega_{TP} < 0, and reduced Landau damping. These may lead to modulational instability. Its growth rate and damping threshold, due to escape of trapped electrons at rate \nu, are calculated for the first time in the short wavelength regime. If the background plasma is in thermal equilibrium, it is shown that this trapped particle modulational instability (TPMI) is not possible when k \lambda_D > 0.46, while for 0.33 < k \lambda_D < 0.46, TPMI requires that the fluctuation wavevector have a component perpendicular to k, the LW wavevector, with \lambda_D the electron Debye length. Its nonlinear evolution leads to self-focusing. Comparison is made with a re-evaluated LW ion acoustic decay instability (LDI): compared to classical estimates, the new LDI threshold is lowered by primary LW \Delta\omega_{TP} since frequency matching leads to wavenumber and hence damping reduction of the daughter LW. For parameters estimates relevant to a recent stimulated Raman scatter experiment (Kline et al., submitted to PRL), the LDI and TPMI thresholds cross in the range 0.28 < k \lambda_D < 0.34, consistent with the observed LDI regime change. However, if \nu exceeds a critical value, estimated to be order 1% of the electron plasma frequency, then TPMI is not possible at any wavenumber