6,063 research outputs found

### Hundred Thousand Degree Gas in the Virgo Cluster of Galaxies

The physical relationship between low-excitation gas filaments at ~10^4 K,
seen in optical line emission, and diffuse X-ray emitting coronal gas at ~10^7
K in the centers of many galaxy clusters is not understood. It is unclear
whether the ~10^4 K filaments have cooled and condensed from the ambient hot
(~10^7 K) medium or have some other origin such as the infall of cold gas in a
merger, or the disturbance of an internal cool reservoir of gas by nuclear
activity. Observations of gas at intermediate temperatures (~10^5-10^6 K) can
potentially reveal whether the central massive galaxies are gaining cool gas
through condensation or losing it through conductive evaporation and hence
identify plausible scenarios for transport processes in galaxy cluster gas.
Here we present spectroscopic detection of ~10^5 K gas spatially associated
with the H-alpha filaments in a central cluster galaxy, M87 in the Virgo
Cluster. The measured emission-line fluxes from triply ionized carbon (CIV 1549
A) and singly ionized helium (HeII 1640 A) are consistent with a model in which
thermal conduction determines the interaction between hot and cold phases.Comment: 10 pages, 2 figures; to appear in ApJ

### Continuous Association Schemes and Hypergroups

Classical finite association schemes lead to a finite-dimensional algebras
which are generated by finitely many stochastic matrices. Moreover, there exist
associated finite hypergroups. The notion of classical discrete association
schemes can be easily extended to the possibly infinite case. Moreover, the
notion of association schemes can be relaxed slightly by using suitably
deformed families of stochastic matrices by skipping the integrality
conditions. This leads to larger class of examples which are again associated
to discrete hypergroups.
In this paper we propose a topological generalization of the notion of
association schemes by using a locally compact basis space $X$ and a family of
Markov-kernels on $X$ indexed by a further locally compact space $D$ where the
supports of the associated probability measures satisfy some partition
property. These objects, called continuous association schemes, will be related
to hypergroup structures on $D$. We study some basic results for this new
notion and present several classes of examples. It turns out that for a given
commutative hypergroup the existence of an associated continuous association
scheme implies that the hypergroup has many features of a double coset
hypergroup. We in particular show that commutative hypergroups, which are
associated with commutative continuous association schemes, carry dual positive
product formulas for the characters. On the other hand, we prove some rigidity
results in particular in the compact case which say that for given spaces $X,D$
there are only a few continuous association schemes

### Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

I construct the spectral function of the Luther-Emery model which describes
one-dimensional fermions with one gapless and one gapped degree of freedom,
i.e. superconductors and Peierls and Mott insulators, by using symmetries,
relations to other models, and known limits. Depending on the relative
magnitudes of the charge and spin velocities, and on whether a charge or a spin
gap is present, I find spectral functions differing in the number of
singularities and presence or absence of anomalous dimensions of fermion
operators. I find, for a Peierls system, one singularity with anomalous
dimension and one finite maximum; for a superconductor two singularities with
anomalous dimensions; and for a Mott insulator one or two singularities without
anomalous dimension. In addition, there are strong shadow bands. I generalize
the construction to arbitrary dynamical multi-particle correlation functions.
The main aspects of this work are in agreement with numerical and Bethe Ansatz
calculations by others. I also discuss the application to photoemission
experiments on 1D Mott insulators and on the normal state of 1D Peierls
systems, and propose the Luther-Emery model as the generic description of 1D
charge density wave systems with important electronic correlations.Comment: Revtex, 27 pages, 5 figures, to be published in European Physical
Journal

### Central limit theorems for multivariate Bessel processes in the freezing regime

Multivariate Bessel processes are classified via associated root systems and
positive multiplicity constants. They describe the dynamics of interacting
particle systems of Calogero-Moser-Sutherland type. Recently, Andraus, Katori,
and Miyashita derived some weak laws of large numbers for these processes for
fixed positive times and multiplicities tending to infinity. In this paper we
derive associated central limit theorems for the root systems of types A, B and
D in an elementary way. In most cases, the limits will be normal distributions,
but in the B-case there are freezing limits where distributions associated with
the root system A or one-sided normal distributions on half-spaces appear. Our
results are connected to central limit theorems of Dumitriu and Edelman for
beta-Hermite and beta-Laguerre ensembles

### A brief introduction to Luttinger liquids

I give a brief introduction to Luttinger liquids. Luttinger liquids are
paramagnetic one-dimensional metals without Landau quasi-particle excitations.
The elementary excitations are collective charge and spin modes, leading to
charge-spin separation. Correlation functions exhibit power-law behavior. All
physical properties can be calculated, e.g. by bosonization, and depend on
three parameters only: the renormalized coupling constant $K_{\rho}$, and the
charge and spin velocities. I also discuss the stability of Luttinger liquids
with respect to temperature, interchain coupling, lattice effects and phonons,
and list important open problems.Comment: 10 pages, 2 figures, to be published in the Proceedings of the
International Winterschool on Electronic Properties of Novel Materials 2000,
Kirchberg, March 4-11, 200

### Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC

In this paper we present explicit product formulas for a continuous
two-parameter family of Heckman-Opdam hypergeometric functions of type BC on
Weyl chambers $C_q\subset \mathbb R^q$ of type $B$. These formulas are related
to continuous one-parameter families of probability-preserving convolution
structures on $C_q\times\mathbb R$. These convolutions on $C_q\times\mathbb R$
are constructed via product formulas for the spherical functions of the
symmetric spaces $U(p,q)/ (U(p)\times SU(q))$ and associated double coset
convolutions on $C_q\times\mathbb T$ with the torus $\mathbb T$. We shall
obtain positive product formulas for a restricted parameter set only, while the
associated convolutions are always norm-decreasing. Our paper is related to
recent positive product formulas of R\"osler for three series of Heckman-Opdam
hypergeometric functions of type BC as well as to classical product formulas
for Jacobi functions of Koornwinder and Trimeche for rank $q=1$

### Dispersion and limit theorems for random walks associated with hypergeometric functions of type BC

The spherical functions of the noncompact Grassmann manifolds
$G_{p,q}(\mathbb F)=G/K$ over the (skew-)fields $\mathbb F=\mathbb R, \mathbb
C, \mathbb H$ with rank $q\ge1$ and dimension parameter $p>q$ can be described
as Heckman-Opdam hypergeometric functions of type BC, where the double coset
space $G//K$ is identified with the Weyl chamber $C_q^B\subset \mathbb R^q$ of
type B. The corresponding product formulas and Harish-Chandra integral
representations were recently written down by M. R\"osler and the author in an
explicit way such that both formulas can be extended analytically to all real
parameters $p\in[2q-1,\infty[$, and that associated commutative convolution
structures $*_p$ on $C_q^B$ exist. In this paper we introduce moment functions
and the dispersion of probability measures on $C_q^B$ depending on $*_p$ and
study these functions with the aid of this generalized integral representation.
Moreover, we derive strong laws of large numbers and central limit theorems for
associated time-homogeneous random walks on $(C_q^B, *_p)$ where the moment
functions and the dispersion appear in order to determine drift vectors and
covariance matrices of these limit laws explicitely. For integers $p$, all
results have interpretations for $G$-invariant random walks on the
Grassmannians $G/K$.
Besides the BC-cases we also study the spaces $GL(q,\mathbb F)/U(q,\mathbb
F)$, which are related to Weyl chambers of type A, and for which corresponding
results hold. For the rank-one-case $q=1$, the results of this paper are
well-known in the context of Jacobi-type hypergroups on $[0,\infty[$.Comment: Extended version of arXiv:1205.4866; some corrections to prior
version. Accepted for publication in J. Theor. Proba

- …