Analytic solutions of the 1D finite coupling delta function Bose gas

An intensive study for both the weak coupling and strong coupling limits of the ground state properties of this classic system is presented. Detailed results for specific values of finite $N$ are given and from them results for general $N$ are determined. We focus on the density matrix and concomitantly its Fourier transform, the occupation numbers, along with the pair correlation function and concomitantly its Fourier transform, the structure factor. These are the signature quantities of the Bose gas. One specific result is that for weak coupling a rational polynomial structure holds despite the transcendental nature of the Bethe equations. All these new results are predicated on the Bethe ansatz and are built upon the seminal works of the past.Comment: 23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by Phys. Rev.

Physical Acoustics

Contains reports on two research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841(42

Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Temporal Regulation of Foregut Development by HTZ-1/H2A.Z and PHA-4/FoxA

The histone variant H2A.Z is evolutionarily conserved and plays an essential role in mice, Drosophila, and Tetrahymena. The essential function of H2A.Z is unknown, with some studies suggesting a role in transcriptional repression and others in activation. Here we show that Caenorhabditis elegans HTZ-1/H2A.Z and the remodeling complex MYS-1/ESA1–SSL-1/SWR1 synergize with the FoxA transcription factor PHA-4 to coordinate temporal gene expression during foregut development. We observe dramatic genetic interactions between pha-4 and htz-1, mys-1, and ssl-1. A survey of transcription factors reveals that this interaction is specific, and thus pha-4 is acutely sensitive to reductions in these three proteins. Using a nuclear spot assay to visualize HTZ-1 in living embryos as organogenesis proceeds, we show that HTZ-1 is recruited to foregut promoters at the time of transcriptional onset, and this recruitment requires PHA-4. Loss of htz-1 by RNAi is lethal and leads to delayed expression of a subset of foregut genes. Thus, the effects of PHA-4 on temporal regulation can be explained in part by recruitment of HTZ-1 to target promoters. We suggest PHA-4 and HTZ-1 coordinate temporal gene expression by modulating the chromatin environment