Quantum Monte Carlo simulations of a particle in a random potential

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for publication in J. of Physics A: Mathematical and Genera

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

Localization of a polymer in random media: Relation to the localization of a quantum particle

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be {\it localized} inside a low minimum of the potential. We show how the end-to-end distance of a polymer which is free to move can be obtained from the density of states of the quantum particle using extreme value statistics. We give a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729 (2000)) in terms of the statistics of localized tail states. Numerical solutions of the variational equations for chains of different length are performed and compared with quenched averages computed directly by using the eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle in a one-dimensional random potential. The quantities investigated are the radius of gyration of a free gaussian chain, its mean square distance from the origin and the end-to-end distance of a tethered chain. The probability distribution for the position of the chain is also investigated. The glassiness of the system is explained and is estimated from the variance of the measured quantities.Comment: RevTex, 44 pages, 13 figure

Magic wavelengths for the 5s−18s5s-18s transition in rubidium

Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms held in an optical dipole trap at a range of wavelengths near a calculated magic value

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

Discovery of a Luminous Quasar in the Nearby Universe

In the course of the Pico dos Dias survey (PDS), we identified the stellar like object PDS456 at coordinates alpha = 17h 28m 19.796s, delta = -14deg 15' 55.87'' (epoch 2000), with a relatively nearby (z = 0.184) and bright (B = 14.69) quasar. Its position at Galactic coordinates l_II = 10.4deg, b_II = +11.2deg, near the bulge of the Galaxy, may explain why it was not detected before. The optical spectrum of PDS456 is typical of a luminous quasar, showing a broad (FWHM ~ 4000 km/s) H_\beta line, very intense FeII lines and a weak [OIII]\lambda5007 line. PDS456 is associated to the infrared source IRAS 17254-1413 with a 60 \mum infrared luminosity L_{60} = 3.8 x 10^{45} erg/s. The relatively flat slopes in the infrared (\alpha(25,60) = -0.33 and \alpha(12,25) = -0.78) and a flat power index in the optical (F_{\nu} \propto \nu^{-0.72}) may indicate a low dust content. A good match between the position of PDS456 and the position of the X-ray source RXS J172819.3-141600 implies an X-ray luminosity L_x = 2.8 x 10^{44} erg/s. The good correlation between the strength of the emission lines in the optical and the X-ray luminosity, as well as the steep optical to X-ray index estimated (\alpha_{ox} = -1.64) suggest that PDS456 is radio quiet. A radio survey previously performed in this region yields an upper limit for radio power at ~ 5 GHz of ~ 2.6 x 10^{30} erg/s/Hz. We estimate the Galactic reddening in this line-of-sight to be A_B \simeq 2.0, implying an absolute magnitude M_B = -26.7 (using H_0 = 75 km s^{-1} Mpc^{-1} and q_0 = 0). In the optical, PDS456 is therefore 1.3 times more luminous than 3C 273 and the most luminous quasar in the nearby (z \leq 0.3) Universe.Comment: 12 pages, LaTeX (aasms4.sty) + 3 figures; accepted for publication in the Astrophysical Journal Letter

Domain wall roughening in dipolar films in the presence of disorder

We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain wall in a thin film with in-plane magnetization, where we consider the contribution of the long-range dipolar interaction beyond the quadratic approximation. We show that such a Hamiltonian is analogous to the Hamiltonian of a one-dimensional polaron in an external random potential. We use a replica variational method to compute the roughening exponent of the domain wall for the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and references 1,2 and 12 were added to conform with the referee's repor

The Formation Rate, Mass and Luminosity Functions of DA White Dwarfs from the Palomar Green Survey

Spectrophotometric observations at high signal-to-noise ratio were obtained of a complete sample of 347 DA white dwarfs from the Palomar Green (PG) Survey. Fits of observed Balmer lines to synthetic spectra calculated from pure-hydrogen model atmospheres were used to obtain robust values of Teff, log g, masses, radii, and cooling ages. The luminosity function of the sample, weighted by 1/Vmax, was obtained and compared with other determinations. The mass distribution of the white dwarfs is derived, after important corrections for the radii of the white dwarfs in this magnitude-limited survey and for the cooling time scales. The formation rate of DA white dwarfs from the PG is estimated to be 0.6x10^(-12) pc^(-3) yr^(-1). Comparison with predictions from a theoretical study of the white dwarf formation rate for single stars indicates that >80% of the high mass component requires a different origin, presumably mergers of lower mass double degenerate stars. In order to estimate the recent formation rate of all white dwarfs in the local Galactic disk, corrections for incompleteness of the PG, addition of the DB-DO white dwarfs, and allowance for stars hidden by luminous binary companions had to be applied to enhance the rate. An overall formation rate of white dwarfs recently in the local Galactic disk of 1.15+/-0.25x10^(-12) pc^(-3) yr^(-1) is obtained. Two recent studies of samples of nearby Galactic planetary nebulae lead to estimates around twice as high. Difficulties in reconciling these determinations are discussed.Comment: 73 pages, 18 figures, accepted for publication in the ApJ Supplemen