5,784 research outputs found
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
plane, where is the particle's mass. The phase diagram is similar to that
of a quantum spin-glass in a transverse field, where the variable
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
Wechselwirkungen zwischen dem deutschen und dem amerikanischen Bildungswesen vom Beginn des 19. Jahrhunderts bis 1945
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 , , and
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
and ions. Moreover, a predicted multiplet spectrum for the heavy
fermion superconductor 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
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