Deconfinement and Chiral Restoration in Hot and Dense Matter

We propose a picture that the chiral phase transition at zero quark mass and the deconfinement transition at infinite quark mass are continuously connected. This gives a simple interpretation on the coincidence of the pseudo-critical temperatures observed in lattice QCD. We discuss a possible dynamical mechanism behind the simultaneous crossovers and show the results in a model study.Comment: Contributed to the XXII International Symposium on Lattice Field Theory (Lattice2004(nonzero)), Batavia, Illinois, Jun 21-26, 200

A New Method of the High Temperature Series Expansion

We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established finite cluster method. Our method emphasizes hidden combinatorial aspects of the high-temperature series expansion, and solves the long-standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites. Series coefficients are expressed in terms of cumulants, which are shown to have the property that all deviations from the lowest-order nonzero cumulant can be expressed in terms of a particular kind of moment expansion. These ``quasi-moments'' can be written in terms of corresponding ``quasi-cumulants'', which enable us to calculate higher-order terms in the high-temperature series expansion. We also present a new technique for obtaining the low-order contributions to specific heat from finite clusters.Comment: 20 pages, 30 figures, to appear in J. Stat. Phy

Relation between color-deconfinement and chiral restoration

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.Comment: Contributed to the XXI International Symposium on Lattice Field Theory (Lattice2003(nonzero)), Tsukuba, July 15-19, 200

Recent Results from Telescope Array

The Telescope Array (TA) is an experiment to observe Ultra-High Energy Cosmic Rays (UHECRs). TA's recent results, the energy spectrum and anisotropy based on the 6-year surface array data, and the primary composition obtained from the shower maximum Xmax are reported. The spectrum demonstrates a clear dip and cutoff. The shape of the spectrum is well described by the energy loss of extra-galactic protons interacting with the cosmic microwave background (CMB). Above the cutoff, a medium-scale (20 degrees radius) flux enhancement was observed near the Ursa-Major. A chance probability of creating this hotspot from the isotropic flux is 4.0 sigma. The measured Xmax is consistent with the primary being proton or light nuclei for energies 10^18.2 eV - 10^19.2 eV.Comment: 8 pages, 15 figures, ISVHECRI2014, CERN, August 18th-22nd, 201

Spectral representation of the particle production out of equilibrium - Schwinger mechanism in pulsed electric fields

We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli-Jordan's and Hadamard's functions. We take an explicit example of a spatially homogeneous scalar theory under pulsed electric fields and investigate the time evolution of the spectral functions. In the out-state we find an oscillatory peak in Hadamard's function as a result of the mixing between positive- and negative-energy waves. The strength of this peak is of the linear order of the Bogoliubov mixing coefficient, whereas the peak corresponding to the Schwinger mechanism is of the quadratic order. Between the in- and the out-states we observe a continuous flow of the spectral peaks together with two transient oscillatory peaks. We also discuss the medium effect at finite temperature and density. We emphasise that the entire structure of the spectral functions conveys rich information on real-time dynamics including the particle production.Comment: 15 pages, 5 figure

Second order asymptotics for Brownian motion in a heavy tailed Poissonian potential

We consider the Feynman-Kac functional associated with a Brownian motion in a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by Pastur (1977) and the first order term of the moment asymptotics was determined. In this paper, both moment and almost sure asymptotics are determined up to the second order. As an application, we also derive the second order asymptotics of the integrated density of states of the corresponding random Schr\"odinger operator.Comment: 29 pages. Minor correction