Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise

We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by means of dynamic field theory and the renormalization group. Using a stochastic Cole--Hopf transformation we derive {\em exact} exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension $d_c = 2 (1+\rho)$. Below the lower critical dimension, there is a line $\rho_*(d)$ marking the stability boundary between the short-range and long-range noise fixed points. For $\rho \geq \rho_*(d)$, the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above $\rho_*(d)$, one has to rely on some perturbational techniques. We discuss the location of this stability boundary $\rho_* (d)$ in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure

Photoelectron spectra of anionic sodium clusters from time-dependent density-functional theory in real-time

We calculate the excitation energies of small neutral sodium clusters in the framework of time-dependent density-functional theory. In the presented calculations, we extract these energies from the power spectra of the dipole and quadrupole signals that result from a real-time and real-space propagation. For comparison with measured photoelectron spectra, we use the ionic configurations of the corresponding single-charged anions. Our calculations clearly improve on earlier results for photoelectron spectra obtained from static Kohn-Sham eigenvalues

The Revealing Dust: Mid-Infrared Activity in Hickson Compact Group Galaxy Nuclei

We present a sample of 46 galaxy nuclei from 12 nearby (z<4500 km/s) Hickson Compact Groups (HCGs) with a complete suite of 1-24 micron 2MASS+Spitzer nuclear photometry. For all objects in the sample, blue emission from stellar photospheres dominates in the near-IR through the 3.6 micron IRAC band. Twenty-five of 46 (54%) galaxy nuclei show red, mid-IR continua characteristic of hot dust powered by ongoing star formation and/or accretion onto a central black hole. We introduce alpha_{IRAC}, the spectral index of a power-law fit to the 4.5-8.0 micron IRAC data, and demonstrate that it cleanly separates the mid-IR active and non-active HCG nuclei. This parameter is more powerful for identifying low to moderate-luminosity mid-IR activity than other measures which include data at rest-frame lambda<3.6 micron that may be dominated by stellar photospheric emission. While the HCG galaxies clearly have a bimodal distribution in this parameter space, a comparison sample from the Spitzer Nearby Galaxy Survey (SINGS) matched in J-band total galaxy luminosity is continuously distributed. A second diagnostic, the fraction of 24 micron emission in excess of that expected from quiescent galaxies, f_{24D}, reveals an additional 3 nuclei to be active at 24 micron. Comparing these two mid-IR diagnostics of nuclear activity to optical spectroscopic identifications from the literature reveals some discrepancies, and we discuss the challenges of distinguishing the source of ionizing radiation in these and other lower luminosity systems. We find a significant correlation between the fraction of mid-IR active galaxies and the total HI mass in a group, and investigate possible interpretations of these results in light of galaxy evolution in the highly interactive system of a compact group environment.Comment: 20 pages, 17 figures (1 color), uses emulateapj. Accepted for publication by Ap

Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnatio

Exploring the Physics of Type Ia Supernovae Through the X-ray Spectra of their Remnants

We present the results of an ongoing project to use the X-ray observations of Type Ia Supernova Remnants to constrain the physical processes involved in Type Ia Supernova explosions. We use the Tycho Supernova Remnant (SN 1572) as a benchmark case, comparing its observed spectrum with models for the X-ray emission from the shocked ejecta generated from different kinds of Type Ia explosions. Both the integrated spectrum of Tycho and the spatial distribution of the Fe and Si emission in the remnant are well reproduced by delayed detonation models with stratified ejecta. All the other Type Ia explosion models fail, including well-mixed deflagrations calculated in three dimensions.Comment: 5 pages, 3 figures, to appear in the proceedings of the "Stellar end products" workshop, 13-15 April 2005, Granada, Spain, ed. M.A. Perez-Torres, Vol. 77 (Jan 2006) of MmSA

Non-adiabatic electron dynamics in time-dependent density-functional theory

Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t), defined as a nonlocal functional of the density n(r',t'). The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], (b) working in a co-moving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. This paper illustrates, compares, and analyzes both non-adiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but in general exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that non-adiabatic effects can become significant, causing the ALDA to break down.Comment: 15 pages, 15 figure