Comments on Black Holes in String Theory

A very brief review is given of some of the developments leading to our current understanding of black holes in string theory. This is followed by a discussion of two possible misconceptions in this subject - one involving the stability of small black holes and the other involving scale radius duality. Finally, I describe some recent results concerning quasinormal modes of black holes in anti de Sitter spacetime, and their implications for strongly coupled conformal field theories (in various dimensions).Comment: 13 pages. Talk given at Strings '99, Potsdam, German

Cosmological string models from Milne spaces and SL(2,Z) orbifold

The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho$, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.Comment: 14 pages, harvma

Diffusion of Neon in White Dwarf Stars

Sedimentation of the neutron rich isotope $^{22}$Ne may be an important source of gravitational energy during the cooling of white dwarf stars. This depends on the diffusion constant for $^{22}$Ne in strongly coupled plasma mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a mixture does not differ greatly from earlier one component plasma results. For strong coupling (coulomb parameter $\Gamma>$ few), $D_i$ has a modest dependence on the charge $Z_i$ of the ion species, $D_i \propto Z_i^{-2/3}$. However $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller $\Gamma$). We conclude that the self-diffusion constant $D_{\rm Ne}$ for $^{22}$Ne in carbon, oxygen, and neon plasma mixtures is accurately known so that uncertainties in $D_{\rm Ne}$ should be unimportant for simulations of white dwarf cooling.Comment: 6 pages, 5 figures, minor changes, Phys. Rev. E in pres

Crystallization of Carbon Oxygen Mixtures in White Dwarf Stars

We determine the phase diagram for dense carbon/ oxygen mixtures in White Dwarf (WD) star interiors using molecular dynamics simulations involving liquid and solid phases. Our phase diagram agrees well with predictions from Ogata et al. and Medin and Cumming and gives lower melting temperatures than Segretain et al. Observations of WD crystallization in the globular cluster NGC 6397 by Winget et al. suggest that the melting temperature of WD cores is close to that for pure carbon. If this is true, our phase diagram implies that the central oxygen abundance in these stars is less than about 60%. This constraint, along with assumptions about convection in stellar evolution models, limits the effective S factor for the $^{12}$C($\alpha,\gamma$)$^{16}$O reaction to S_{300} <= 170 keV barns.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres

Using penalized likelihood to select parameters in a random coefficients multinomial logit model

This paper is about estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters, some of which may be zero. The paper gives conditions under which, with probability approaching 1 as the sample size increases, penalized maximum likelihood (PML) estimation with the adaptive LASSO (AL) penalty distinguishes correctly between zero and non-zero parameters. The paper also gives conditions under which PML reduces the asymptotic mean-square estimation error of any continuously differentiable function of the model’s parameters. The paper describes a method for computing PML estimates and presents the results of Monte Carlo experiments that illustrate their performance. It also presents the results of PML estimation of a random coefficients logit model of choice among brands of butter and margarine in the British groceries market

Comments on Black Holes in Matrix Theory

The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes black strings stretched across the longitudinal direction, near the transition where black strings become unstable to the formation of black holes. It is argued that the appropriate dynamics on the other (black hole) side of the transition is that of the zero modes of the corresponding super Yang-Mills theory. A suggestive mean field theory argument is given for the entropy of black holes in all dimensions. Consequences of the analysis for matrix theory and the holographic principle are discussed.Comment: 15 pages, harvmac, minor errors correcte

Neutrino Scattering in Heterogeneous Supernova Plasmas

Neutrinos in core collapse supernovae are likely trapped by neutrino-nucleus elastic scattering. Using molecular dynamics simulations, we calculate neutrino mean free paths and ion-ion correlation functions for heterogeneous plasmas. Mean free paths are systematically shorter in plasmas containing a mixture of ions compared to a plasma composed of a single ion species. This is because neutrinos can scatter from concentration fluctuations. The dynamical response function of a heterogeneous plasma is found to have an extra peak at low energies describing the diffusion of concentration fluctuations. Our exact molecular dynamics results for the static structure factor reduce to the Debye Huckel approximation, but only in the limit of very low momentum transfers.Comment: 11 pages, 13 figure

Delta Excitations in Neutrino-Nucleus Scattering

We derive the contribution of $\Delta$-h excitations to quasielastic charged-current neutrino-nucleus scattering in the framework of relativistic mean-field theory. We discuss the effect of $\Delta$ production on the determination of the axial mass $M_A$ in neutrino scattering experiments.Comment: 14 pages, revtex, 3 postscript figures (available upon request

Strong Correlations in Actinide Redox Reactions

Reduction-oxidation (redox) reactions of the redox couples An(VI)/An(V), An(V)/An(IV), and An(IV)/An(III), where An is an element in the family of early actinides (U, Np, and Pu), as well as Am(VI)/Am(V) and Am(V)/Am(III), are modeled by combining density functional theory with a generalized Anderson impurity model that accounts for the strong correlations between the 5f electrons. Diagonalization of the Anderson impurity model yields improved estimates for the redox potentials and the propensity of the actinide complexes to disproportionate.Comment: 17 pages, 10 figure, 3 tables. Corrections and clarifications; this version has been accepted for publication in The Journal of Chemical Physic

Position-dependent exact-exchange energy for slabs and semi-infinite jellium

The position-dependent exact-exchange energy per particle $\varepsilon_x(z)$ (defined as the interaction between a given electron at $z$ and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove analytically and numerically that in the vacuum region far away from the surface $\varepsilon_{x}^{\text{Slab}}(z \to \infty) \to - e^{2}/2z$, {\it independent} of the bulk electron density, which is exactly half the corresponding exact-exchange potential $V_{x}(z \to \infty) \to - e^2/z$ [Phys. Rev. Lett. {\bf 97}, 026802 (2006)] of density-functional theory, as occurs in the case of finite systems. The fitting of $\varepsilon_{x}^{\text{Slab}}(z)$ to a physically motivated image-like expression is feasible, but the resulting location of the image plane shows strong finite-size oscillations every time a slab discrete energy level becomes occupied. For a semi-infinite jellium, the asymptotic behavior of $\varepsilon_{x}^{\text{SI}}(z)$ is somehow different. As in the case of jellium slabs $\varepsilon_{x}^{\text{SI}}(z \to \infty)$ has an image-like behavior of the form $\propto - e^2/z$, but now with a density-dependent coefficient that in general differs from the slab universal coefficient 1/2. Our numerical estimates for this coefficient agree with two previous analytical estimates for the same. For an arbitrary finite thickness of a jellium slab, we find that the asymptotic limits of $\varepsilon_{x}^{\text{Slab}}(z)$ and $\varepsilon_{x}^{\text{SI}}(z)$ only coincide in the low-density limit ($r_s \to \infty$), where the density-dependent coefficient of the semi-infinite jellium approaches the slab {\it universal} coefficient 1/2.Comment: 26 pages, 7 figures, to appear in Phys. Rev.