Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata I

The Ammount of Interstellar Carbon Locked in Solid Hydrogenated Amorphous Carbon

We review the literature and present new experimental data to determine the amount of carbon likely to be locked in form of solid hydrogenated amorphous carbon (HAC) grains. We conclude on the basis of a thorough analysis of the intrinsic strength of the C-H stretching band at 3.4 micron that between 10 and 80 ppM H of carbon is in the form of HAC grains. We show that it is necessary to know the level of hydrogenation (H/C) of the interstellar HAC to determine more precisely the amount of carbon it ties up. We present optical constants, photoluminescence spectroscopy, and IR absorption spectroscopy for a particular HAC sample that is shown to have a 3.4 micron absorption feature that is quantatively consistent with that observed in the diffuse interstellar medium.Comment: This paper is 14 pages long with 5 figures and will appear in the 1 December 1999 issue of Ap

The Excitation of Extended Red Emission: New Constraints on its Carrier From HST Observations of NGC 7023

The carrier of the dust-associated photoluminescence process causing the extended red emission (ERE) in many dusty interstellar environments remains unidentified. Several competing models are more or less able to match the observed broad, unstructured ERE band. We now constrain the character of the ERE carrier further by determining the wavelengths of the radiation that initiates the ERE. Using the imaging capabilities of the Hubble Space Telescope, we have resolved the width of narrow ERE filaments appearing on the surfaces of externally illuminated molecular clouds in the bright reflection nebula NGC 7023 and compared them with the depth of penetration of radiation of known wavelengths into the same cloud surfaces. We identify photons with wavelengths shortward of 118 nm as the source of ERE initiation, not to be confused with ERE excitation, however. There are strong indications from the well-studied ERE in the Red Rectangle nebula and in the high-|b| Galactic cirrus that the photon flux with wavelengths shortward of 118 nm is too small to actually excite the observed ERE, even with 100% quantum efficiency. We conclude, therefore, that ERE excitation results from a two-step process. While none of the previously proposed ERE models can match these new constraints, we note that under interstellar conditions most polycyclic aromatic hydrocarbon (PAH) molecules are ionized to the di-cation stage by photons with E > 10.5 eV and that the electronic energy level structure of PAH di-cations is consistent with fluorescence in the wavelength band of the ERE. Therefore, PAH di-cations deserve further study as potential carriers of the ERE. (abridged)Comment: Accepted for Publication in the Ap

Critical behaviour of the Rouse model for gelling polymers

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_{s}$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.

The Photophysics of the Carrier of Extended Red Emission

Interstellar dust contains a component which reveals its presence by emitting a broad, unstructured band of light in the 540 to 950 nm wavelength range, referred to as Extended Red Emission (ERE). The presence of interstellar dust and ultraviolet photons are two necessary conditions for ERE to occur. This is the basis for suggestions which attribute ERE to an interstellar dust component capable of photoluminescence. In this study, we have collected all published ERE observations with absolute-calibrated spectra for interstellar environments, where the density of ultraviolet photons can be estimated reliably. In each case, we determined the band-integrated ERE intensity, the wavelength of peak emission in the ERE band, and the efficiency with which absorbed ultraviolet photons are contributing to the ERE. The data show that radiation is not only driving the ERE, as expected for a photoluminescence process, but is modifying the ERE carrier as manifested by a systematic increase in the ERE band's peak wavelength and a general decrease in the photon conversion efficiency with increasing densities of the prevailing exciting radiation. The overall spectral characteristics of the ERE and the observed high quantum efficiency of the ERE process are currently best matched by the recently proposed silicon nanoparticle (SNP) model. Using the experimentally established fact that ionization of semiconductor nanoparticles quenches their photoluminescence, we proceeded to test the SNP model by developing a quantitative model for the excitation and ionization equilibrium of SNPs under interstellar conditions for a wide range of radiation field densities.Comment: 42 p., incl. 8 fig. Accepted for publication by Ap

The Dust in Lyman Break Galaxies

We present our analysis of UV attenuation by internal dust of a large sample (N=906 galaxies) of Lyman Break Galaxies (LBGs). Using spectral energy distributions (SEDs) from the P\'EGASE galaxy spectral evolution model we apply dust attenuation corrections to the G-R colors using the Witt & Gordon (2000) models for radiative transfer in dusty galactic environments to arrive at the UV attenuation factors. We show that the dust in the LBGs exhibit SMC-like characteristics rather than MW-like, and that the dust geometry in these systems is most likely to be represented by a clumpy shell configuration. We show that the attenuation factor exhibits a pronounced dependence on the luminosity of the LBG, a_{1600}\propto (L/L_\sun)^\alpha, where $0.5\leq\alpha\leq1.5$. The exponent $\alpha$ depends on the initial parameters of the stellar population chosen to model the galaxies and the dust properties. We find that the luminosity weighted average attenuation factor is likely to be in the range from $5.7-18.5$, which is consistent with the upper limits to the star formation rate at $2<z<4$ set by the FIR background. This implies that the current UV/optical surveys do detect the bulk of the star formation during the epoch $2<z<4$, but require substantial correction for internal dust attenuation.Comment: 17 pages, 12 figures, uses AASTEX, accepted for publication in the Astrophysical Journa

Critical Dynamics of Gelation

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $k=\phi-\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\phi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor changes

Force-Extension Relations for Polymers with Sliding Links

Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable size. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation: The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus--de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.Comment: 4 pages, 5 figures; accepted to Phys. Rev. E (Brief Report

Viscoelasticity near the gel-point: a molecular dynamics study

We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e. particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed throughout the system and imposed with probability p. At a critical concentration of bonds, p_c approximately equal to 0.2488 for f=6, a gel is formed and the shear viscosity \eta diverges according to \eta ~ (p_c-p)^{-s}. We find s is approximately 0.7 in agreement with some experiments and with a recent theoretical prediction based on Rouse dynamics of phantom chains. The diffusion constant decreases as the gel point is approached but does not display a well-defined power law.Comment: 4 pages, 4 figure