The Impact of Isospin Breaking on the Distribution of Transition Probabilities

In the present paper we investigate the effect of symmetry breaking in the statistical distributions of reduced transition amplitudes and reduced transition probabilities. These quantities are easier to access experimentally than the components of the eigenvectors and were measured by Adams et al. for the electromagnetic transitions in ^{26}Al. We focus on isospin symmetry breaking described by a matrix model where both, the Hamiltonian and the electromagnetic operator, break the symmetry. The results show that for partial isospin conservation, the statistical distribution of the reduced transition probability can considerably deviate from the Porter-Thomas distribution.Comment: 16 pages, 8 figures, submitted to PR

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Strangeness production time and the K+/pi+ horn

We construct a hadronic kinetic model which describes production of strange particles in ultrarelativistic nuclear collisions in the energy domain of SPS. We test this model on description of the sharp peak in the excitation function of multiplicity ratio K+/pi+ and demonstrate that hadronic model reproduces these data rather well. The model thus must be tested on other types of data in order to verify the hypothesis that deconfinement sets in at lowest SPS energies.Comment: proceedings of Hot Quarks 0

Chiral Symmetry and light resonances in hot and dense matter

We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and $\rho$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear matter and Heavy-Ion Collision experiments, such as $\rho$ mass scaling vs broadening from dilepton spectra and chiral restoration signals in the $\sigma$ channel. We also elaborate on the molecular nature of $\pi\pi$ resonances.Comment: 14 pages, 14 figures. Contribution to Hard Probes 2008, Illa de A Toxa, Spain, June 8th-14th 200

Photon interferometry and size of the hot zone in relativistic heavy ion collisions

The parameters obtained from the theoretical analysis of the single photon spectra observed by the WA98 collaboration at SPS energies have been used to evaluate the two photon correlation functions. The single photon spectra and the two photon correlations at RHIC energies have also been evaluated, taking into account the effects of the possible spectral change of hadrons in a thermal bath. We find that the ratio $R_{side}/R_{out} \sim 1$ for SPS and $R_{side}/R_{out} <1$ for RHIC energy.Comment: text changed, figures adde

Electromagnetic Probes

A review is presented of dilepton and real photon measurements in relativistic heavy ion collisions over a very broad energy range from the low energies of the BEVALAC up to the highest energies available at RHIC. The dileptons cover the invariant mass range \mll = 0 - 2.5 GeV/c$^2$, i.e. the continuum at low and intermediate masses and the light vector mesons, $\rho, \omega, \phi$. The review includes also measurements of the light vector mesons in elementary reactions.Comment: To be published in Landolt-Boernstein Volume 1-23A; 40 pages, 24 figures. Final version updated with small changes to the text, updated references and updated figure

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

New hadrons as ultra-high energy cosmic rays

Ultra-high energy cosmic ray (UHECR) protons produced by uniformly distributed astrophysical sources contradict the energy spectrum measured by both the AGASA and HiRes experiments, assuming the small scale clustering of UHECR observed by AGASA is caused by point-like sources. In that case, the small number of sources leads to a sharp exponential cutoff at the energy E<10^{20} eV in the UHECR spectrum. New hadrons with mass 1.5-3 GeV can solve this cutoff problem. For the first time we discuss the production of such hadrons in proton collisions with infrared/optical photons in astrophysical sources. This production mechanism, in contrast to proton-proton collisions, requires the acceleration of protons only to energies E<10^{21} eV. The diffuse gamma-ray and neutrino fluxes in this model obey all existing experimental limits. We predict large UHE neutrino fluxes well above the sensitivity of the next generation of high-energy neutrino experiments. As an example we study hadrons containing a light bottom squark. These models can be tested by accelerator experiments, UHECR observatories and neutrino telescopes.Comment: 17 pages, revtex style; v2: shortened, as to appear in PR

Colossal dielectric constants in transition-metal oxides

Many transition-metal oxides show very large ("colossal") magnitudes of the dielectric constant and thus have immense potential for applications in modern microelectronics and for the development of new capacitance-based energy-storage devices. In the present work, we thoroughly discuss the mechanisms that can lead to colossal values of the dielectric constant, especially emphasising effects generated by external and internal interfaces, including electronic phase separation. In addition, we provide a detailed overview and discussion of the dielectric properties of CaCu3Ti4O12 and related systems, which is today's most investigated material with colossal dielectric constant. Also a variety of further transition-metal oxides with large dielectric constants are treated in detail, among them the system La2-xSrxNiO4 where electronic phase separation may play a role in the generation of a colossal dielectric constant.Comment: 31 pages, 18 figures, submitted to Eur. Phys. J. for publication in the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and Ordering of Microscopic Degrees of Freedom

Hadronic properties of the S_{11}(1535) studied by electroproduction off the deuteron

Properties of excited baryonic states are investigated in the context of electroproduction of baryon resonances off the deuteron. In particular, the hadronic radii and the compositeness of baryon resonances are studied for kinematic situations in which their hadronic reinteraction is the dominant contribution. Specifically, we study the reaction $d(e,e'S_{11})N$ at $Q^2\ge 1 GeV^2$ for kinematics in which the produced hadronic state reinteracts predominantly with the spectator nucleon. A comparison of constituent quark model and effective chiral Lagrangian calculations of the $S_{11}$ shows substantial sensitivity to the structure of the produced resonance.Comment: 24 pages, 5 figure