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

Disorder effects in the quantum Heisenberg model: An Extended Dynamical mean-field theory analysis

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin-liquid (where the local spin susceptibility has a non-integer power-low frequency and/or temperature dependence), in the present case this behavior is more elusive unless disorder is very small. This is because the spin-glass transition temperature leaves only an intermediate temperature regime where the system can display the spin-liquid behavior, which turns out to be more apparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure

The Stellar Populations and Evolution of Lyman Break Galaxies

Using deep near-IR and optical observations of the HDF-N from the HST NICMOS and WFPC2 and from the ground, we examine the spectral energy distributions (SEDs) of Lyman break galaxies (LBGs) at 2.0 < z < 3.5. The UV-to-optical rest-frame SEDs of the galaxies are much bluer than those of present-day spiral and elliptical galaxies, and are generally similar to those of local starburst galaxies with modest amounts of reddening. We use stellar population synthesis models to study the properties of the stars that dominate the light from LBGs. Under the assumption that the star-formation rate is continuous or decreasing with time, the best-fitting models provide a lower bound on the LBG mass estimates. LBGs with ``L*'' UV luminosities are estimated to have minimum stellar masses ~ 10^10 solar masses, or roughly 1/10th that of a present-day L* galaxy. By considering the effects of a second component of maximally-old stars, we set an upper bound on the stellar masses that is ~ 3-8 times the minimum estimate. We find only loose constraints on the individual galaxy ages, extinction, metallicities, initial mass functions, and prior star-formation histories. We find no galaxies whose SEDs are consistent with young (< 10^8 yr), dust-free objects, which suggests that LBGs are not dominated by ``first generation'' stars, and that such objects are rare at these redshifts. We also find that the typical ages for the observed star-formation events are significantly younger than the time interval covered by this redshift range (~ 1.5 Gyr). From this, and from the relative absence of candidates for quiescent, non-star-forming galaxies at these redshifts in the NICMOS data, we suggest that star formation in LBGs may be recurrent, with short duty cycles and a timescale between star-formation events of < 1 Gyr. [Abridged]Comment: LaTeX, 37 pages, 21 figures. Accepted for publication in the Astrophysical Journa

Phase Transitions of the Flux Line Lattice in High-Temperature Superconductors with Weak Columnar and Point Disorder

We study the effects of weak columnar and point disorder on the vortex-lattice phase transitions in high temperature superconductors. The combined effect of thermal fluctuations and of quenched disorder is investigated using a simplified cage model. For columnar disorder the problem maps into a quantum particle in a harmonic + random potential. We use the variational approximation to show that columnar and point disorder have opposite effect on the position of the melting line as observed experimentally. Replica symmetry breaking plays a role at the transition into a vortex glass at low temperatures.Comment: 4 pages in 2 columns format + 2 eps figs included, uses RevTeX and multicol.st