1,068 research outputs found
Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills
We investigate critical slowing down in the local updating continuous-time
Quantum Monte Carlo method by relating the finite size scaling of Fisher Zeroes
to the dynamically generated gap, through the scaling of their respective
critical exponents. As we comment, the nonlinear sigma model representation
derived through the hamiltonian of our lattice spin model can also be used to
give a effective treatment of planar anomalous dimensions in N=4 SYM. We
present scaling arguments from our FSS analysis to discuss quantum corrections
and recent 2-loop results, and further comment on the prospects of extending
this approach for calculating higher twist parton distributions.Comment: Lattice 2004(spin), Fermilab, June 21-26, 2004; 3 pages, 4 figure
Coronal Fe XIV Emission During the Whole Heliosphere Interval Campaign
Solar Cycle 24 is having a historically long and weak start. Observations of
the Fe XIV corona from the Sacramento Peak site of the National Solar
Observatory show an abnormal pattern of emission compared to observations of
Cycles 21, 22, and 23 from the same instrument. The previous three cycles have
shown a strong, rapid "Rush to the Poles" (previously observed in polar crown
prominences and earlier coronal observations) in the parameter N(t,l,dt)
(average number of Fe XIV emission features per day over dt days at time t and
latitude l). Cycle 24 displays a weak, intermittent, and slow "Rush" that is
apparent only in the northern hemisphere. If the northern Rush persists at its
current rate, evidence from the Rushes in previous cycles indicates that solar
maximum will occur in early 2013 or late 2012, at least in the northern
hemisphere. At lower latitudes, solar maximum previously occurred when the time
maximum of N(t,l,365) reached approximately 20{\deg} latitude. Currently, this
parameter is at or below 30{\deg}and decreasing in latitude. Unfortunately, it
is difficult at this time to calculate the rate of decrease in N(t,l,365).
However, the southern hemisphere could reach 20{\deg} in 2011. Nonetheless,
considering the levels of activity so far, there is a possibility that the
maximum could be indiscernibleComment: 8 pages, 4 figures; Solar Physics Online First, 2011
http://www.springerlink.com/content/b5kl4040k0626647
A note on the Painleve analysis of a (2+1) dimensional Camassa-Holm equation
We investigate the Painleve analysis for a (2+1) dimensional Camassa-Holm
equation. Our results show that it admits only weak Painleve expansions. This
then confirms the limitations of the Painleve test as a test for complete
integrability when applied to non-semilinear partial differential equations.Comment: Chaos, Solitons and Fractals (Accepted for publication
Sufficient Covariate, Propensity Variable and Doubly Robust Estimation
Statistical causal inference from observational studies often requires
adjustment for a possibly multi-dimensional variable, where dimension reduction
is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a
popular approach to such reduction. We address causal inference within Dawid's
decision-theoretic framework, where it is essential to pay attention to
sufficient covariates and their properties. We examine the role of a propensity
variable in a normal linear model. We investigate both population-based and
sample-based linear regressions, with adjustments for a multivariate covariate
and for a propensity variable. In addition, we study the augmented inverse
probability weighted estimator, involving a combination of a response model and
a propensity model. In a linear regression with homoscedasticity, a propensity
variable is proved to provide the same estimated causal effect as multivariate
adjustment. An estimated propensity variable may, but need not, yield better
precision than the true propensity variable. The augmented inverse probability
weighted estimator is doubly robust and can improve precision if the propensity
model is correctly specified
Numerical study of duality and universality in a frozen superconductor
The three-dimensional integer-valued lattice gauge theory, which is also
known as a "frozen superconductor," can be obtained as a certain limit of the
Ginzburg-Landau theory of superconductivity, and is believed to be in the same
universality class. It is also exactly dual to the three-dimensional XY model.
We use this duality to demonstrate the practicality of recently developed
methods for studying topological defects, and investigate the critical behavior
of the phase transition using numerical Monte Carlo simulations of both
theories. On the gauge theory side, we concentrate on the vortex tension and
the penetration depth, which map onto the correlation lengths of the order
parameter and the Noether current in the XY model, respectively. We show how
these quantities behave near the critical point, and that the penetration depth
exhibits critical scaling only very close to the transition point. This may
explain the failure of superconductor experiments to see the inverted XY model
scaling.Comment: 17 pages, 18 figures. Updated to match the version published in PRB
(http://link.aps.org/abstract/PRB/v67/e014525) on 27 Jan 200
Directed geometrical worm algorithm applied to the quantum rotor model
We discuss the implementation of a directed geometrical worm algorithm for
the study of quantum link-current models. In this algorithm Monte Carlo updates
are made through the biased reptation of a worm through the lattice. A directed
algorithm is an algorithm where, during the construction of the worm, the
probability for erasing the immediately preceding part of the worm, when adding
a new part,is minimal. We introduce a simple numerical procedure for minimizing
this probability. The procedure only depends on appropriately defined local
probabilities and should be generally applicable. Furthermore we show how
correlation functions, C(r,tau) can be straightforwardly obtained from the
probability of a worm to reach a site (r,tau) away from its starting point
independent of whether or not a directed version of the algorithm is used.
Detailed analytical proofs of the validity of the Monte Carlo algorithms are
presented for both the directed and un-directed geometrical worm algorithms.
Results for auto-correlation times and Green functions are presented for the
quantum rotor model.Comment: 11 pages, 9 figures, v2 : Additional results and data calculated at
an incorrect chemical potential replaced. Conclusions unchange
Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder
The effect of a weak three-dimensional (3d) isotropic laser speckle disorder
on various thermodynamic properties of a dilute Bose gas is considered at zero
temperature. First, we summarize the derivation of the autocorrelation function
of laser speckles in 1d and 2d following the seminal work of Goodman. The goal
of this discussion is to show that a Gaussian approximation of this function,
proposed in some recent papers, is inconsistent with the general background of
laser speckle theory. Then we propose a possible experimental realization for
an isotropic 3d laser speckle potential and derive its corresponding
autocorrelation function. Using a Fourier transform of that function, we
calculate both condensate depletion and sound velocity of a Bose-Einstein
condensate as disorder ensemble averages of such a weak laser speckle potential
within a perturbative solution of the Gross-Pitaevskii equation. By doing so,
we reproduce the expression of the normalfluid density obtained earlier within
the treatment of Landau. This physically transparent derivation shows that
condensate particles, which are scattered by disorder, form a gas of
quasiparticles which is responsible for the normalfluid component
On the Computational Complexity of Measuring Global Stability of Banking Networks
Threats on the stability of a financial system may severely affect the
functioning of the entire economy, and thus considerable emphasis is placed on
the analyzing the cause and effect of such threats. The financial crisis in the
current and past decade has shown that one important cause of instability in
global markets is the so-called financial contagion, namely the spreading of
instabilities or failures of individual components of the network to other,
perhaps healthier, components. This leads to a natural question of whether the
regulatory authorities could have predicted and perhaps mitigated the current
economic crisis by effective computations of some stability measure of the
banking networks. Motivated by such observations, we consider the problem of
defining and evaluating stabilities of both homogeneous and heterogeneous
banking networks against propagation of synchronous idiosyncratic shocks given
to a subset of banks. We formalize the homogeneous banking network model of
Nier et al. and its corresponding heterogeneous version, formalize the
synchronous shock propagation procedures, define two appropriate stability
measures and investigate the computational complexities of evaluating these
measures for various network topologies and parameters of interest. Our results
and proofs also shed some light on the properties of topologies and parameters
of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic
Scaling critical behavior of superconductors at zero magnetic field
We consider the scaling behavior in the critical domain of superconductors at
zero external magnetic field. The first part of the paper is concerned with the
Ginzburg-Landau model in the zero magnetic field Meissner phase. We discuss the
scaling behavior of the superfluid density and we give an alternative proof of
Josephson's relation for a charged superfluid. This proof is obtained as a
consequence of an exact renormalization group equation for the photon mass. We
obtain Josephson's relation directly in the form , that
is, we do not need to assume that the hyperscaling relation holds. Next, we
give an interpretation of a recent experiment performed in thin films of
. We argue that the measured mean field like
behavior of the penetration depth exponent is possibly associated with a
non-trivial critical behavior and we predict the exponents and
for the correlation lenght and specific heat, respectively. In the
second part of the paper we discuss the scaling behavior in the continuum dual
Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau
model, we discuss the continuum dual version by considering a family of
scalings characterized by a parameter introduced such that
, where is the bare mass of the magnetic
induction field. We discuss the difficulties in identifying the renormalized
magnetic induction mass with the photon mass. We show that the only way to have
a critical regime with is having , that
is, with having the scaling behavior of the renormalized photon mass.Comment: RevTex, 15 pages, no figures; the subsection III-C has been removed
due to a mistak
Aharonov-Bohm Physics with Spin II: Spin-Flip Effects in Two-dimensional Ballistic Systems
We study spin effects in the magneto-conductance of ballistic mesoscopic
systems subject to inhomogeneous magnetic fields. We present a numerical
approach to the spin-dependent Landauer conductance which generalizes recursive
Green function techniques to the case with spin. Based on this method we
address spin-flip effects in quantum transport of spin-polarized and
-unpolarized electrons through quantum wires and various two-dimensional
Aharonov-Bohm geometries. In particular, we investigate the range of validity
of a spin switch mechanism recently found which allows for controlling spins
indirectly via Aharonov-Bohm fluxes. Our numerical results are compared to a
transfer-matrix model for one-dimensional ring structures presented in the
first paper (Hentschel et al., submitted to Phys. Rev. B) of this series.Comment: 29 pages, 15 figures. Second part of a series of two article
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