20,810 research outputs found
Moments of a single entry of circular orthogonal ensembles and Weingarten calculus
Consider a symmetric unitary random matrix
from a circular orthogonal ensemble. In this paper, we study moments of a
single entry . For a diagonal entry we give the explicit
values of the moments, and for an off-diagonal entry we give leading
and subleading terms in the asymptotic expansion with respect to a large matrix
size . Our technique is to apply the Weingarten calculus for a
Haar-distributed unitary matrix.Comment: 17 page
Incommensurate magnetism in cuprate materials
In the low doping region an incommensurate magnetic phase is observed in
LSCO. By means of the composite operator method we show that the single-band 2D
Hubbard model describes the experimental situation. In the higher doping
region, where experiments are not available, the incommensurability is
depressed owing to the van Hove singularity near the Fermi level. A
proportionality between the incommensurability amplitude and the critical
temperature is predicted, suggesting a close relation between superconductivity
and incommensurate magnetism.Comment: 4 pages, 5 figures in one Postscript file, RevTe
Why Two Renormalization Groups are Better than One
The advantages of using more than one renormalization group (RG) in problems
with more than one important length scale are discussed. It is shown that: i)
using different RG's can lead to complementary information, i.e. what is very
difficult to calculate with an RG based on one flow parameter may be much more
accessible using another; ii) using more than one RG requires less physical
input in order to describe via RG methods the theory as a function of its
parameters; iii) using more than one RG allows one to solve problems with more
than one diverging length scale. The above points are illustrated concretely in
the context of both particle physics and statistical physics using the
techniques of environmentally friendly renormalization. Specifically, finite
temperature theory, an Ising-type system in a film geometry, an
Ising-type system in a transverse magnetic field, the QCD coupling constant at
finite temperature and the crossover between bulk and surface critical
behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn
Straight Round the Twist: Frustration and Chirality in Smectics-A
Frustration is a powerful mechanism in condensed matter systems, driving both
order and co plexity. In smectics, the frustration between macroscopic
chirality and equally spaced layers generates textures characterised by a
proliferation of defects. In this article, we study several different ground
states of the chiral Landau-de Gennes free energy for a smectic liquid crystal.
The standard theory finds the twist grain boundary (TGB) phase to be the ground
state for chiral type II smectics. However, for very highly chiral systems, the
hierarchical helical nanofilament (HN) phase can form and is stable over the
TGB.Comment: 9 pages, 3 figures, submitted to J. Interface Focu
Dark energy from modified gravity with Lagrange multipliers
We study scalar-tensor theory, k-essence and modified gravity with Lagrange
multiplier constraint which role is to reduce the number of degrees of freedom.
Dark Energy cosmology of different types (CDM, unified inflation with
DE, smooth non-phantom/phantom transition epoch) is reconstructed in such
models. It is shown that mathematical equivalence between scalar theory and
gravity is broken due to presence of constraint. The cosmological
dynamics of gravity is modified by the second function dictated
by the constraint. Dark Energy cosmology is defined by this function while
standard function is relevant for local tests (modification of newton
regime). A general discussion on the role of Lagrange multipliers to make
higher-derivative gravity canonical is developed.Comment: LaTeX 12 pages, discussion is improve
Patterns on a Roll: A Method for Continuous Feed Nanoprinting
Exploiting elastic instability in thin films has proven a robust method for
creating complex patterns and structures across a wide range of lengthscales.
Even the simplest of systems, an elastic membrane with a lattice of pores,
under mechanical strain, generates complex patterns featuring long-range
orientational order. When we promote this system to a curved surface, in
particular, a cylindrical membrane, a novel set of features, patterns and
broken symmetries appears. The newfound periodicity of the cylinder allows for
a novel continuous method for nanoprinting.Comment: 4 pages, 4 figure
ASCA observations of massive medium-distant clusters of galaxies. II
We have selected seven medium-distant clusters of galaxies (z ~ 0.1 - 0.3)
for multi-wavelength observations with the goal of investigating their
dynamical state. Following Paper I (Pierre et al. 1999) which reported the ASCA
results about two of them, we present here the analysis of the ASCA
observations of the other five clusters; RXJ1023.8-2715 (A3444),
RXJ1031.6-2607, RXJ1050.5-0236 (A1111), RXJ1203.2-2131(A1451), and
RXJ1314.5-2517. Except for RXJ1031.6, whose X-ray emission turned out to be
dominated by an AGN, the ASCA spectra are well fitted by a one-temperature thin
thermal plasma model. We compare the temperature-luminosity relation of our
clusters with that of nearby ones (z<0.1). Two clusters, RXJ1050.5 and
RXJ1023.8, show larger luminosities than the bulk of clusters at similar
temperatures, which suggests the presence of a cooling flow. The temperature
vs. iron-abundance relationship of our sample is consistent with that of nearby
clusters.Comment: 9 pages, 20 figures, A&AS in pres
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