Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

Testing statistical bounds on entanglement using quantum chaos

Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems, investigated recently, entails an universal distribution of the eigenvalues of the reduced density matrices. We demonstrate that these distributions are realized in quantized chaotic systems by using a model of two coupled and kicked tops. We derive an explicit statistical universal bound on entanglement, that is also valid for the case of unequal dimensionality of the Hilbert spaces involved, and show that this describes well the bounds observed using composite quantized chaotic systems such as coupled tops.Comment: 5 pages, 3 figures, to appear in PRL. New title. Revised abstract and some changes in the body of the pape

Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

High Resolution CO and H2 Molecular Line Imaging of a Cometary Globule in the Helix Nebula

We report high resolution imaging of a prominent cometary globule in the Helix nebula in the CO J=1-0 (2.6 mm) and H2 v=1-0 S(1) (2.12 micron) lines. The observations confirm that globules consist of dense condensations of molecular gas embedded in the ionized nebula. The head of the globule is seen as a peak in the CO emission with an extremely narrow line width (0.5 km/s) and is outlined by a limb-brightened surface of H2 emission facing the central star and lying within the photo-ionized halo. The emission from both molecular species extends into the tail region. The presence of this extended molecular emission provides new constraints on the structure of the tails, and on the origin and evolution of the globules.Comment: 12 pages, 3 figures. To appear in The Astrophysical Journal Letter

A Framework for the Landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background and contains metastable de Sitter space as an intermediate state.Comment: 29+13 pages, 25 figures; v2: minor corrections, references adde

Distribution of the Riemann zeros represented by the Fermi gas

The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.Comment: 7 page

Eigenvector localization for random band matrices with power law band width

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.Comment: 30 pages; corrected typo

Fluctuation properties of strength functions associated with giant resonances

We performed fluctuation analysis by means of the local scaling dimension for the strength function of the isoscalar (IS) and the isovector (IV) giant quadrupole resonances (GQR) in $^{40}$Ca, where the strength functions are obtained by the shell model calculation within up to the 2p2h configurations. It is found that at small energy scale, fluctuation of the strength function almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit. On the other hand, we found a deviation from the GOE limit at the intermediate energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results imply that different types of fluctuations coexist at different energy scales. Detailed analysis strongly suggests that GOE fluctuation at small energy scale is due to the complicated nature of 2p2h states and that fluctuation at the intermediate energy scale is associated with the spreading width of the Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure