Replica field theory for a polymer in random media

In this paper we revisit the problem of a (non self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM). As noticed by Cates and Ball (CB) there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ``localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the radius of gyration, g is the strength of the disorder, \mu is the spring constant associated with the confining potential and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln(V) as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d<2 and for large V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The 1-step replica symmetry breaking solution is crucial for obtaining the above results.Comment: Revtex, 32 page

Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle like an an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use the replica method, and are able to solve the model and obtain its phase diagram in the $T - (\hbar^2/m)$ plane, where $m$ is the particle's mass. The phase diagram is similar to that of a quantum spin-glass in a transverse field, where the variable $\hbar^2/m$ plays the role of the transverse field. The glassy phase is characterized by replica-symmetry-breaking. The quantum transition at zero temperature is also discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate file figures.u

NICMOS Observations of Low-Redshift Quasar Host Galaxies

We have obtained Near-Infrared Camera and Multi-Object Spectrometer images of 16 radio quiet quasars observed as part of a project to investigate the ``luminosity/host-mass limit.'' The limit results were presented in McLeod, Rieke, & Storrie-Lombardi (1999). In this paper, we present the images themselves, along with 1- and 2-dimensional analyses of the host galaxy properties. We find that our model-independent 1D technique is reliable for use on ground-based data at low redshifts; that many radio-quiet quasars live in deVaucouleurs-law hosts, although some of the techniques used to determine host type are questionable; that complex structure is found in many of the hosts, but that there are some hosts that are very smooth and symmetric; and that the nuclei radiate at ~2-20% of the Eddington rate based on the assumption that all galaxies have central black holes with a constant mass fraction of 0.6%. Despite targeting hard-to-resolve hosts, we have failed to find any that imply super-Eddington accretion rates.Comment: To appear in ApJ, 28 pages including degraded figures. Download the paper with full-resolutio figures from http://www.astro.wellesley.edu/kmcleod/mm.p

A comparison of the optical properties of radio-loud and radio-quiet quasars

We have made radio observations of 87 optically selected quasars at 5 GHz with the VLA in order to measure the radio power for these objects and hence determine how the fraction of radio-loud quasars varies with redshift and optical luminosity. The sample has been selected from the recently completed Edinburgh Quasar Survey and covers a redshift range of 0.3 < z < 1.5 and an optical absolute magnitude range of -26.5 < M_{B} < -23.5 (h, q_{0} = 1/2). We have also matched up other existing surveys with the FIRST and NVSS radio catalogues and combined these data so that the optical luminosity-redshift plane is now far better sampled than previously. We have fitted a model to the probability of a quasar being radio-loud as a function of absolute magnitude and redshift and from this model infer the radio-loud and radio-quiet optical luminosity functions. The radio-loud optical luminosity function is featureless and flatter than the radio-quiet one. It evolves at a marginally slower rate if quasars evolve by density evolution, but the difference in the rate of evolutions of the two different classes is much less than was previously thought. We show, using Monte-Carlo simulations, that the observed difference in the shape of the optical luminosity functions can be partly accounted for by Doppler boosting of the optical continuum of the radio-loud quasars and explain how this can be tested in the future.Comment: 33 pages, 9 postscript figures, uses the AAS aaspp4 LaTeX style file, to appear in the 1 February 1999 issue of The Astrophysical Journa

Counting Giant Gravitons in AdS_3

We quantize the set of all quarter BPS brane probe solutions in global AdS_3 \times S^3 \times T^4/K3 found in arxiv:0709.1168 [hep-th]. We show that, generically, these solutions give rise to states in discrete representations of the SL(2,R) WZW model on AdS_3. Our procedure provides us with a detailed description of the low energy 1/4 and 1/2 BPS sectors of string theory on this background. The 1/4 BPS partition function jumps as we move off the point in moduli space where the bulk theta angle and NS-NS fields vanish. We show that generic 1/2 BPS states are protected because they correspond to geodesics rather than puffed up branes. By exactly quantizing the simplest of the probes above, we verify our description of 1/4 BPS states and find agreement with the known spectrum of 1/2 BPS states of the boundary theory. We also consider the contribution of these probes to the elliptic genus and discuss puzzles, and their possible resolutions, in reproducing the elliptic genus of the symmetric product.Comment: 47 pages; (v2) references and minor clarifications adde

The dusty environment of Quasars. Far-IR properties of Optical Quasars

We present the ISO far-IR photometry of a complete sub-sample of optically selected bright quasars belonging to two complete surveys selected through multicolour (U,B,V,R,I) techniques. The ISOPHOT camera on board of the ISO Satellite was used to target these quasars at wavelengths of 7.3, 11.5, 60, 100 and 160 micron. Almost two thirds of the objects were detected at least in one ISOPHOT band. The detection rate is independent of the source redshift, very likely due to the negative K-correction of the far-IR thermal emission. More than a half of the optically selected QSOs show significant emission between 4 and 100 micron in the quasar rest-frame. These fluxes have a very likely thermal origin, although in a few objects an additional contribution from a non-thermal component is plausible in the long wavelength bands. In a colour-colour diagram these objects span a wide range of properties from AGN-dominated to ULIRG-like. The far-IR composite spectrum of the quasar population presents a broad far-IR bump between 10 and 30 micron and a sharp drop at wavelengths greater than 100 micron in the quasar restframe. The amount of energy emitted in the far-IR, is on average a few times larger than that emitted in the blue and the ratio L(FIR)/L(B) increases with the bolometric luminosity. Objects with fainter blue magnitudes have larger ratios between the far-IR (wavelengths > 60 micron) fluxes and the blue band flux, which is attributed to extinction by dust around the central source. No relation between the blue absolute magnitude and the dust colour temperature is seen, suggesting that the dominant source of FIR energy could be linked to a concurrent starburst rather than to gravitational energy produced by the central engine.Comment: Astronomical Journal, in pres

Optical/Near-Infrared Imaging of Infrared-Excess Palomar-Green QSOs

Ground-based high spatial-resolution (FWHM < 0.3-0.8") optical and near-infrared imaging (0.4-2.2um) is presented for a complete sample of optically selected Palomar-Green QSOs with far-infrared excesses at least as great as those of "warm" AGN-like ultraluminous infrared galaxies (L_ir/L_big-blue-bump > 0.46). In all cases, the host galaxies of the QSOs were detected and most have discernable two-dimensional structure. The QSO host galaxies and the QSO nuclei are similar in magnitude at H-band. H-band luminosities of the hosts range from 0.5-7.5 L* with a mean of 2.3 L*, and are consistent with those found in ULIGs. Both the QSO nuclei and the host galaxies have near-infrared excesses, which may be the result of dust associated with the nucleus and of recent dusty star formation in the host. These results suggest that some, but not all, optically-selected QSOs may have evolved from an infrared-active state triggered by the merger of two similarly-sized L* galaxies, in a manner similar to that of the ultraluminous infrared galaxies.Comment: Aastex format, 38 pages, 4 tables, 10 figures. Higher quality figures are available in JPG forma

Radio Properties of z>4 Optically-Selected Quasars

We report on two programs to address differential evolution between the radio-loud and radio-quiet quasar populations at high (z>4) redshift. Both programs entail studying the radio properties of optically-selected quasars. First, we have observed 32 optically-selected, high-redshift (z>4) quasars with the VLA at 6 cm (5 GHz). These sources comprise a statistically complete and well-understood sample. We detect four quasars above our 3-sigma limit of ~0.15 mJy, which is sufficiently sensitive to detect all radio-loud quasars at the probed redshift range. Second, we have correlated 134 z>4 quasars, comprising all such sources that we are aware of as of mid-1999, with FIRST and NVSS. These two recent 1.4 GHz VLA sky surveys reach 3-sigma limits of approximately 0.6 mJy and 1.4 mJy respectively. We identify a total of 15 z>4 quasars, of which six were not previously known to be radio-loud. The depth of these surveys does not reach the radio-loud/radio-quiet demarcation luminosity density (L(1.4 GHz) = 10^32.5 h(50)^(-2) ergs/s/Hz) at the redshift range considered; this correlation therefore only provides a lower limit to the radio-loud fraction of quasars at high-redshift. The two programs together identify eight new radio-loud quasars at z>4, a significant increase over the seven currently in the published literature. We find no evidence for radio-loud fraction depending on optical luminosity for -25 > M_B > -28 at z~2, or for -26>M_B>-28 at z>4. Our results also show no evolution in the radio-loud fraction between z~2 and z>4 (-26>M_B>-28).Comment: 19 pages, 7 figures; to appear in The Astronomical Journal (April 2000

The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase transition will appear at zero branching rate limit belonging to the same universality class as that of the dynamical two-offspring (2-BARW2) model. This class persists even if the branching is biased towards one of the species. If the two systems are not coupled by branching but hard-core interaction is allowed only the transition will occur at finite branching rate belonging to the usual 1+1 dimensional directed percolation class.Comment: 3 pages, 3 figures include

Magnetism and local distortions near carbon impurity in γ\gamma-iron

Local perturbations of crystal and magnetic structure of $\gamma$-iron near carbon interstitial impurity is investigated by {\it ab initio} electronic structure calculations. It is shown that the carbon impurity creates locally a region of ferromagnetic ordering with substantial tetragonal distortions. Exchange integrals and solution enthalpy are calculated, the latter being in a very good agreement with experimental data. Effect of the local distortions on the carbon-carbon interactions in $\gamma$-iron is discussed.Comment: 4 pages 3 figures. Final version, accepted to Phys.Rev. Let