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

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

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

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

Calculation of Effective Coulomb Interaction for Pr3+Pr^{3+}, U4+U^{4+}, and UPt3UPt_3

In this paper, the Slater integrals for a screened Coulomb interaction of the the Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, good agreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$ and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavy fermion superconductor $UPt_3$ is shown with a calculated Coulomb U of 1.6 eV. These effective Coulomb interactions, which are quite simple to calculate, should be useful inputs to further many-body calculations in correlated electron metals.Comment: 8 pages, revtex, 3 uuencoded postscript figure