Eigenvalue correlations in QCD with a chemical potential

We discuss a new Random Matrix Model for QCD with a chemical potential that is based on the symmetries of the Dirac operator and can be solved exactly for all eigenvalue correlations for any number of flavors. In the microscopic limit of small energy levels the results should be an accurate description of QCD. This new model can also be scaled so that all physical observables remain at their $\mu=0$ values until a first order chiral restoration transition is reached. This gives a more realistic model for the QCD phase diagram than previous RMM. We also mention how the model might aid in determining the phase diagram of QCD from future numerical simulations.Comment: 3 pages, 3 figures, Lattice2004(non-zero

QCD critical point and event-by-event fluctuations in heavy ion collisions

A summary of work done in collaboration with K. Rajagopal and E. Shuryak. We show how heavy ion collision experiments, in particular, event-by-event fluctuation measurements, can lead to the discovery of the critical point on the phase diagram of QCD.Comment: 4 pages. Summary of work done in collaboration with K. Rajagopal and E. Shuryak (hep-ph/9903292). To be published in the proceedings of Quark Matter 99, Torino, Italy, May 10-14, 199

Universal correlations in spectra of the lattice QCD Dirac operator

Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as $12^4$. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal Ensemble for Wilson fermions. In both cases long range spectral fluctuations are strongly suppressed: the variance of a sequence of levels containing $n$ eigenvalues on average is given by $\Sigma_2(n) \sim 2 (\log n)/\beta\pi^2$ ($\beta$ is equal to 4 and 1, respectively) instead of $\Sigma_2(n) = n$ for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions which differs from Wilson fermions (with the continuum anti-unitary symmetry). For $N_c = 3$, we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.Comment: Talk present at LATTICE96(chirality in QCD), 3 pages, Late

Universal fluctuations in spectra of the lattice Dirac operator

Recently, Kalkreuter obtained the complete Dirac spectrum for an $SU(2)$ lattice gauge theory with dynamical staggered fermions on a $12^4$ lattice for $\beta =1.8$ and $\beta=2.8$. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble. In particular, long range fluctuations are strongly suppressed: the variance of a sequence of levels containing $n$ eigenvalues on average is given by $\Sigma_2(n) \sim\frac 1{2\pi^2}(\log n + {\rm const.})$ instead of $\Sigma_2(n) = n$ for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions which differs from the continuuum theory. For $N_c = 3$ we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.Comment: 8 pages + 3 figures (will be faxed on request

The Economic Value of Wild Resources to the Indigenous Community of the Wallis Lakes Catchment

There is currently a growing policy interest in the effects of the regulatory environment on the ability of Indigenous people to undertake customary harvesting of wild resources. This Discussion Paper develops and describes a methodology that can be used to estimate the economic benefi ts derived from the use of wild resources. The methodology and the survey instrument that was developed were pilot tested with the Indigenous community of the Wallis Lake catchment. The harvesting of wild resources for consumption makes an important contribution to the livelihoods of Indigenous people living in this area.Indigenous; harvesting of wild resources; natural resource management

Contextual normalization applied to aircraft gas turbine engine diagnosis

Diagnosing faults in aircraft gas turbine engines is a complex problem. It involves several tasks, including rapid and accurate interpretation of patterns in engine sensor data. We have investigated contextual normalization for the development of a software tool to help engine repair technicians with interpretation of sensor data. Contextual normalization is a new strategy for employing machine learning. It handles variation in data that is due to contextual factors, rather than the health of the engine. It does this by normalizing the data in a context-sensitive manner. This learning strategy was developed and tested using 242 observations of an aircraft gas turbine engine in a test cell, where each observation consists of roughly 12,000 numbers, gathered over a 12 second interval. There were eight classes of observations: seven deliberately implanted classes of faults and a healthy class. We compared two approaches to implementing our learning strategy: linear regression and instance-based learning. We have three main results. (1) For the given problem, instance-based learning works better than linear regression. (2) For this problem, contextual normalization works better than other common forms of normalization. (3) The algorithms described here can be the basis for a useful software tool for assisting technicians with the interpretation of sensor data

Quantum chaos in QCD at finite temperature

We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the nearest-neighbor spacing distribution $P(s)$ for various values of $\beta$ both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at "Lattice 97", to appear in the proceeding