7,325 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
Interrelated structure of high altitude atmospheric profiles
A preliminary development of a mathematical model to compute probabilities of thermodynamic profiles is presented. The model assumes an exponential expression for pressure and utilizes the hydrostatic law and equation of state in the determination of density and temperature. It is shown that each thermodynamic variable can be factored into the produce of steady state and perturbation functions. The steady state functions have profiles similar to those of the 1962 standard atmosphere while the perturbation functions oscillate about 1. Limitations of the model and recommendations for future work are presented
Large time dynamics and aging of a polymer chain in a random potential
We study the out-of-equilibrium large time dynamics of a gaussian polymer
chain in a quenched random potential. The dynamics studied is a simple Langevin
dynamics commonly referred to as the Rouse model. The equations for the
two-time correlation and response function are derived within the gaussian
variational approximation. In order to implement this approximation faithfully,
we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical
action. For a short ranged correlated random potential the equations are solved
analytically in the limit of large times using certain assumptions concerning
the asymptotic behavior. Two possible dynamical behaviors are identified
depending upon the time separation- a stationary regime and an aging regime. In
the stationary regime time translation invariance holds and so is the
fluctuation dissipation theorem. The aging regime which occurs for large time
separations of the two-time correlation functions is characterized by history
dependence and the breakdown of certain equilibrium relations. The large time
limit of the equations yields equations among the order parameters that are
similar to the equations obtained in the statics using replicas. In particular
the aging solution corresponds to the broken replica solution. But there is a
difference in one equation that leads to important consequences for the
solution. The stationary regime corresponds to the motion of the polymer inside
a local minimum of the random potential, whereas in the aging regime the
polymer hops between different minima. As a byproduct we also solve exactly the
dynamics of a chain in a random potential with quadratic correlations.Comment: 21 pages, RevTeX
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
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
Analysis of Gamma Rays and Cosmic Muons with a Single Detector
In this paper, we report on the construction and upgrade of a 2002 Lawrence Berkeley National Laboratory (LBNL) Quanknet Cosmic Muons Detector. By adapting this model, we modify the electronics and mechanics to achieve a highly efficient gamma-ray and cosmic-ray detector. Each detector module uses a one-inch-thick scintillator, attached to a photomultiplier tube (PMT) and mounted on a solid aluminum frame. A mechanical support was designed to allow flexible positioning between the two modules. The detector uses scintillation to transform passing radiation into detectable photons that are guided toward a photocathode surface of the PMT, triggering the release of photoelectrons that are then amplified to yield measurable electronic signals. The modules were connected to an electronics section that compared the signals from the two PMTs and logically determined if they were coincidence events. A data-collection device was added for faster count rates and to enable counts for extended times ranging from a few hours to days as needed. Count rates were taken at a variety of distances from the radioactive source, 60Co (cobalt), which produced two gamma rays and a beta particle. To investigate the isotropic behavior of radiation, two detection modules were adjusted to different angles of rotation with respect to each other, and the coincidence counts were measured. The coincidence counts from the modules set at various angles were consistent throughout the angular spectrum, and only lead shielding visibly reduced the number of counts from the radioactive source. The inverse-square-law behavior of radiation has also been considered. The results were such that the number of counts decreased as a function of increasing distance from the source. Furthermore, positioning the detector to point toward the sky in different orientations, we measured cosmic ray muon flux as the angle from the vertical was decreased. In doing so, we scanned different patches of the atmosphere. For the optimum operation during the detection phase, we plateaued both PMTs to single out their best operating gain voltage while eliminating false background noise signals. The detector is more efficient and adaptable in collecting both gamma rays and cosmic-ray muon-flux information
Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O in the presence of straight and of tilted columnar defects
In this paper we use London Langevin molecular dynamics simulations to
investigate the vortex matter melting transition in the highly anisotropic
high-temperature superconductor material Bi_2Sr_2CaCu_2O in the
presence of low concentration of columnar defects (CDs). We reproduce with
further details our previous results obtained by using Multilevel Monte Carlo
simulations that showed that the melting of the nanocrystalline vortex matter
occurs in two stages: a first stage melting into nanoliquid vortex matter and a
second stage delocalization transition into a homogeneous liquid. Furthermore,
we report on new dynamical measurements in the presence of a current that
identifies clearly the irreversibility line and the second stage delocalization
transition. In addition to CDs aligned along the c-axis we also simulate the
case of tilted CDs which are aligned at an angle with respect to the applied
magnetic field. Results for CDs tilted by with respect to c-axis
show that the locations of the melting and delocalization transitions are not
affected by the tilt when the ratio of flux lines to CDs remains constant. On
the other hand we argue that some dynamical properties and in particular the
position of the irreversibility line should be affected.Comment: 13 pages, 11 figure
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