6,004 research outputs found
Statistical Physics and Light-Front Quantization
Light-front quantization has important advantages for describing relativistic
statistical systems, particularly systems for which boost invariance is
essential, such as the fireball created in a heavy ion collisions. In this
paper we develop light-front field theory at finite temperature and density
with special attention to quantum chromodynamics. We construct the most general
form of the statistical operator allowed by the Poincare algebra and show that
there are no zero-mode related problems when describing phase transitions. We
then demonstrate a direct connection between densities in light-front thermal
field theory and the parton distributions measured in hard scattering
experiments. Our approach thus generalizes the concept of a parton distribution
to finite temperature. In light-front quantization, the gauge-invariant Green's
functions of a quark in a medium can be defined in terms of just 2-component
spinors and have a much simpler spinor structure than the equal-time fermion
propagator. From the Green's function, we introduce the new concept of a
light-front density matrix, whose matrix elements are related to forward and to
off-diagonal parton distributions. Furthermore, we explain how thermodynamic
quantities can be calculated in discretized light-cone quantization, which is
applicable at high chemical potential and is not plagued by the
fermion-doubling problem.Comment: 30 pages, 3 figures; v2: Refs. added, minor changes, accepted for
publication in PR
On the well-posedness of the stochastic Allen-Cahn equation in two dimensions
White noise-driven nonlinear stochastic partial differential equations
(SPDEs) of parabolic type are frequently used to model physical and biological
systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak
solutions to these equations are well established in one dimension, the
situation is different for d \geq 2. Despite their popularity in the applied
sciences, higher dimensional versions of these SPDE models are generally
assumed to be ill-posed by the mathematics community. We study this discrepancy
on the specific example of the two dimensional Allen-Cahn equation driven by
additive white noise. Since it is unclear how to define the notion of a weak
solution to this equation, we regularize the noise and introduce a family of
approximations. Based on heuristic arguments and numerical experiments, we
conjecture that these approximations exhibit divergent behavior in the
continuum limit. The results strongly suggest that a series of published
numerical studies are problematic: shrinking the mesh size in these simulations
does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics
(Dec 2011
Inference for High-dimensional Differential Correlation Matrices
Motivated by differential co-expression analysis in genomics, we consider in
this paper estimation and testing of high-dimensional differential correlation
matrices. An adaptive thresholding procedure is introduced and theoretical
guarantees are given. Minimax rate of convergence is established and the
proposed estimator is shown to be adaptively rate-optimal over collections of
paired correlation matrices with approximately sparse differences. Simulation
results show that the procedure significantly outperforms two other natural
methods that are based on separate estimation of the individual correlation
matrices. The procedure is also illustrated through an analysis of a breast
cancer dataset, which provides evidence at the gene co-expression level that
several genes, of which a subset has been previously verified, are associated
with the breast cancer. Hypothesis testing on the differential correlation
matrices is also considered. A test, which is particularly well suited for
testing against sparse alternatives, is introduced. In addition, other related
problems, including estimation of a single sparse correlation matrix,
estimation of the differential covariance matrices, and estimation of the
differential cross-correlation matrices, are also discussed.Comment: Accepted for publication in Journal of Multivariate Analysi
Corruption and Political Interest: Empirical Evidence at the Micro Level
The topic of corruption has recently attracted a great deal of attention, yet there is still a lack of micro level empirical evidence regarding the determinants of corruption. Furthermore, the present literature has not investigated the effects of political interest on corruption despite the interesting potential of this link. We address these deficiencies by analyzing a cross-section of individuals, using the World Values Survey. We explore the determinants of corruption through two dependent variables (perceived corruption and the justifiability of corruption). The impact of political interest on corruption is explored through three different proxies, presenting empirical evidence at both the cross-country level and the within-country level. The results of the multivariate analysis suggest that political interest has an impact on corruption controlling for a large number of factors.Corruption, Political Interest, Social Norms
Aggregation functions: Means
The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).
Phonons and related properties of extended systems from density-functional perturbation theory
This article reviews the current status of lattice-dynamical calculations in
crystals, using density-functional perturbation theory, with emphasis on the
plane-wave pseudo-potential method. Several specialized topics are treated,
including the implementation for metals, the calculation of the response to
macroscopic electric fields and their relevance to long wave-length vibrations
in polar materials, the response to strain deformations, and higher-order
responses. The success of this methodology is demonstrated with a number of
applications existing in the literature.Comment: 52 pages, 14 figures, submitted to Review of Modern Physic
Emergence of macroscopic directed motion in populations of motile colloids
From the formation of animal flocks to the emergence of coordinate motion in
bacterial swarms, at all scales populations of motile organisms display
coherent collective motion. This consistent behavior strongly contrasts with
the difference in communication abilities between the individuals. Guided by
this universal feature, physicists have proposed that solely alignment rules at
the individual level could account for the emergence of unidirectional motion
at the group level. This hypothesis has been supported by agent-based
simulations. However, more complex collective behaviors have been
systematically found in experiments including the formation of vortices,
fluctuating swarms, clustering and swirling. All these model systems
predominantly rely on actual collisions to display collective motion. As a
result, the potential local alignment rules are entangled with more complex,
often unknown, interactions. The large-scale behavior of the populations
therefore depends on these uncontrolled microscopic couplings. Here, we
demonstrate a new phase of active matter. We reveal that dilute populations of
millions of colloidal rollers self-organize to achieve coherent motion along a
unique direction, with very few density and velocity fluctuations. Identifying
the microscopic interactions between the rollers allows a theoretical
description of this polar-liquid state. Comparison of the theory with
experiment suggests that hydrodynamic interactions promote the emergence of
collective motion either in the form of a single macroscopic flock at low
densities, or in that of a homogenous polar phase at higher densities.
Furthermore, hydrodynamics protects the polar-liquid state from the giant
density fluctuations. Our experiments demonstrate that genuine physical
interactions at the individual level are sufficient to set homogeneous active
populations into stable directed motion
Phase Structure of Z(3)-Polyakov-Loop Models
We study effective lattice actions describing the Polyakov loop dynamics
originating from finite-temperature Yang-Mills theory. Starting with a
strong-coupling expansion the effective action is obtained as a series of
Z(3)-invariant operators involving higher and higher powers of the Polyakov
loop, each with its own coupling. Truncating to a subclass with two couplings
we perform a detailed analysis of the statistical mechanics involved. To this
end we employ a modified mean field approximation and Monte Carlo simulations
based on a novel cluster algorithm. We find excellent agreement of both
approaches concerning the phase structure of the theories. The phase diagram
exhibits both first and second order transitions between symmetric,
ferromagnetic and anti-ferromagnetic phases with phase boundaries merging at
three tricritical points. The critical exponents nu and gamma at the continuous
transition between symmetric and anti-ferromagnetic phases are the same as for
the 3-state Potts model.Comment: 20 pages, 22 figure
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