Two-Flavor Staggered Fermion Thermodynamics at N_t = 12

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover a determination of the induced baryon charge and baryon susceptibility, the scalar susceptibility, and the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for N_t = 4, 6, and 8, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature dependent ``constituent quark free energy.''Comment: LaTeX 25 pages, 15 Postscript figure

Light hadrons with improved staggered quarks: approaching the continuum limit

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0- meson propagators, and we make a preliminary mass computation for a radially excited 0- meson.Comment: 43 pages, 16 figure

Baryon Density Correlations in High Temperature Hadronic Matter

As part of an ongoing effort to characterize the high temperature phase of QCD, in a numerical simulation using the staggered fermion scheme, we measure the quark baryon density in the vicinity of a fixed test quark at high temperature and compare it with similar measurements at low temperature and at the crossover temperature. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at $T = 0.75\ T_c$ the total induced quark number shows a surprisingly large component attributable to baryonic screening. A companion simulation of a simple flux tube model produces similar results and also suggests a plausible phenomenological scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.Comment: 26 pp, RevTeX, 12 postscript figures, combined in a single shell archive file. (Also available in 13 postscript files by anonymous ftp from einstein.physics.utah.edu, /pub/milc/paper.sh.Z.

Magnetic Fields in Quasar Cores II

Multi-frequency polarimetry with the Very Long Baseline Array (VLBA) telescope has revealed absolute Faraday Rotation Measures (RMs) in excess of 1000 rad/m/m in the central regions of 7 out of 8 strong quasars studied (e.g., 3C 273, 3C 279, 3C 395). Beyond a projected distance of ~20 pc, however, the jets are found to have |RM| < 100 rad/m/m. Such sharp RM gradients cannot be produced by cluster or galactic-scale magnetic fields, but rather must be the result of magnetic fields organized over the central 1-100 pc. The RMs of the sources studied to date and the polarization properties of BL Lacs, quasars and galaxies are shown to be consistent so far with the predictions of unified schemes. The direct detection of high RMs in these quasar cores can explain the low fractional core polarizations usually observed in quasars at centimeter wavelengths as the result of irregularities in the Faraday screen on scales smaller than the telescope beam. Variability in the RM of the core is reported for 3C 279 between observations taken 1.5 years apart, indicating that the Faraday screen changes on that timescale, or that the projected superluminal motion of the inner jet components samples a new location in the screen with time. Either way, these changes in the Faraday screen may explain the dramatic variability in core polarization properties displayed by quasars.Comment: Accepted to the ApJ. 27 pages, 9 figures including figure 6 in colo

Multiconfigurational Hartree-Fock theory for identical bosons in a double well

Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of double well barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.Comment: 21 pages, 13 figure

String amplitudes in arbitrary dimensions

We calculate gravitational dressed tachyon correlators in non critcal dimensions. The 2D gravity part of our theory is constrained to constant curvature. Then scaling dimensions of gravitational dressed vertex operators are equal to their bare conformal dimensions. Considering the model as d+2 dimensional critical string we calculate poles of generalized Shapiro-Virasoro amplitudes.Comment: 14 page

Continuous-time quantum walk on integer lattices and homogeneous trees

This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

QCD equation of state at non-zero chemical potential

We present our new results for the QCD equation of state at nonzero chemical potential at N_t=6 and compare them with N_t=4. We use the Taylor expansion method with terms up to sixth order in simulations with 2+1 flavors of improved asqtad quarks along a line of constant physics with m_l=0.1 m_s and approximately physical strange quark mass m_s.Comment: 7 pages, 10 figures, presented at Lattice 2008 (Nonzero Temperature and Density), College of William and Mary, Williamsburg, V

Tube Models for Rubber-Elastic Systems

In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model for the confinement of long paths in polymer networks which is partially due to crosslinking and partially due to entanglements. Our model describes a non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube models. We present results for the macroscopic elastic properties as well as for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres