7,491 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
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
Empirical Research Plan: Effects of Sketching on Program Comprehension
Sketching is an important means of communication in software engineering
practice. Yet, there is little research investigating the use of sketches. We
want to contribute a better understanding of sketching, in particular its use
during program comprehension. We propose a controlled experiment to investigate
the effectiveness and efficiency of program comprehension with the support of
sketches as well as what sketches are used in what way.Comment: 5 pages, 0 figures, Proc. International Conference on Agile Software
Development (XP'16). Volume 251 of the book series Lecture Notes in Business
Information Processing (LNBIP). Springer, 201
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
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
Of mice and men: Sparse statistical modeling in cardiovascular genomics
In high-throughput genomics, large-scale designed experiments are becoming
common, and analysis approaches based on highly multivariate regression and
anova concepts are key tools. Shrinkage models of one form or another can
provide comprehensive approaches to the problems of simultaneous inference that
involve implicit multiple comparisons over the many, many parameters
representing effects of design factors and covariates. We use such approaches
here in a study of cardiovascular genomics. The primary experimental context
concerns a carefully designed, and rich, gene expression study focused on
gene-environment interactions, with the goals of identifying genes implicated
in connection with disease states and known risk factors, and in generating
expression signatures as proxies for such risk factors. A coupled exploratory
analysis investigates cross-species extrapolation of gene expression
signatures--how these mouse-model signatures translate to humans. The latter
involves exploration of sparse latent factor analysis of human observational
data and of how it relates to projected risk signatures derived in the animal
models. The study also highlights a range of applied statistical and genomic
data analysis issues, including model specification, computational questions
and model-based correction of experimental artifacts in DNA microarray data.Comment: Published at http://dx.doi.org/10.1214/07-AOAS110 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The importance of radio sources in accounting for the highest mass black holes
The most massive black holes lie in the most massive elliptical galaxies, and
at low-z all radio-loud AGNs lie in giant ellipticals. This strongly suggests a
link between radio-loudness and black hole mass. We argue that the increase in
the radio-loud fraction with AGN luminosity in optically-selected quasar
samples is consistent with this picture. We also use the ratio of black holes
today to quasars at z~2 to conclude that the most bolometrically-luminous AGN,
either radio-loud or radio quiet, are constrained to have lifetimes <~10^8 yr.
If radio sources are associated with black holes of >~10^9 M_sun at all
redshifts, then the same lifetime constraint applies to all radio sources with
luminosities above L_5GHz ~ 10^24 W/Hz/sr.Comment: 6 pages, 2 figures. To appear in "Lifecycles of Radio Galaxies", ed
J. Biretta et al., New Astronomy Review
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
Dynamical solutions of a quantum Heisenberg spin glass model
We consider quantum-dynamical phenomena in the ,
infinite-range quantum Heisenberg spin glass. For a fermionic generalization of
the model we formulate generic dynamical self-consistency equations. Using the
Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic
states we study in particular the isotropic model variant on the spin space.
Two complementary approximation schemes are applied: one restricts the quantum
spin dynamics to a manageable number of Matsubara frequencies while the other
employs an expansion in terms of the dynamical local spin susceptibility. We
accurately determine the critical temperature of the spin glass to
paramagnet transition. We find that the dynamical correlations cause an
increase of by 2% compared to the result obtained in the spin-static
approximation. The specific heat exhibits a pronounced cusp at .
Contradictory to other reports we do not observe a maximum in the -curve
above .Comment: 8 pages, 7 figure
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