Pfaffian Expressions for Random Matrix Correlation Functions

It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian expressions in terms of the corresponding skew orthogonal polynomials. Then we clarify the relation to Eynard and Mehta's determinant formula for hermitian matrix models and explain how the evaluation is simplified in the cases related to the classical orthogonal polynomials. Applications of Pfaffian formulas to random matrix theory and other fields are also mentioned.Comment: 28 page

1/S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet

We study the effects of quantum fluctuations on excitation spectra in the two-dimensional Heisenberg antiferromagnet by means of the 1/S expansion. We calculate the spin-wave dispersion and the transverse dynamical structure factor up to the second order of 1/S in comparison with inelastic neutron scattering experiments. The spin-wave energy at momentum $(\pi,0)$ is found to be about 2% smaller than that at $(\pi/2,\pi/2)$ due to the second-order correction. In addition, we study the dimensional crossover from two dimensions to one dimension by weakening exchange couplings in one direction. It is found that the second-order correction becomes large with approaching the quasi-one dimensional situation and makes the spin-wave energy approach to the des Cloizeaux-Pearson boundary for $S=1/2$. The transverse dynamical structure factor is also calculated up to the second order of 1/S. It is shown that the intensity of spin-wave peak is strongly reduced while the intensity of three-spin-wave continuum becomes large and exceeds that of the spin-wave peak in the quasi-one dimensional situation.Comment: 20 pages, 6 figures, revised text, added curves in Figs. 3 and 6 for J'/J=0.075 and corrected typos in Table

ALMA reveals a chemically evolved submillimeter galaxy at z=4.76

The chemical properties of high-z galaxies provide important information to constrain galaxy evolutionary scenarios. However, widely-used metallicity diagnostics based on rest-frame optical emission lines are not usable for heavily dust-enshrouded galaxies (such as Sub-Millimeter Galaxies; SMGs), especially at z>3. Here we focus on the flux ratio of the far-infrared fine-structure emission lines [NII]205um and [CII]158um to assess the metallicity of high-z SMGs. Through ALMA cycle 0 observations, we have detected the [NII]205um emission in a strongly [CII]-emitting SMG, LESS J033229.4-275619 at z=4.76. The velocity-integrated [NII]/[CII] flux ratio is 0.043 +/- 0.008. This is the first measurement of the [NII]/[CII] flux ratio in high-z galaxies, and the inferred flux ratio is similar to the ratio observed in the nearby universe (~0.02-0.07). The velocity-integrated flux ratio and photoionization models suggest that the metallicity in this SMG is consistent with solar, implying the chemical evolution has progressed very rapidly in this system at z=4.76. We also obtain a tight upper limit on the CO(12-11) transition, which translates into CO(12-11)/CO(2-1) <3.8 (3 sigma). This suggests that the molecular gas clouds in LESS J033229.4-275619 are not affected significantly by the radiation field emitted by the AGN in this system.Comment: 5 pages, 3 figures, accepted for publication in Astronomy and Astrophysics Letter

Parametric correlations versus fidelity decay: the symmetry breaking case

We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.Comment: 8 pages, 8 figure

Spectral Universality of Real Chiral Random Matrix Ensembles

We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories ($\beta =1$) by relating the kernel of the correlations functions for $\beta =1$ to the kernel of chiral Random Matrix Theories with complex matrix elements ($\beta = 2$), which is already known to be universal. Our proof is based on a novel asymptotic property of the skew-orthogonal polynomials: an integral over the corresponding wavefunctions oscillates about half its asymptotic value in the region of the bulk of the zeros. This result solves the puzzle that microscopic universality persists in spite of contributions to the microscopic correlators from the region near the largest zero of the skew-orthogonal polynomials. Our analytical results are illustrated by the numerical construction of the skew-orthogonal polynomials for an $x^4$ probability potential.Comment: 27 pages, 4 figures, Latex, corrected typo

The Color-Flavor Transformation and Lattice QCD

We present the color-flavor transformation for gauge group SU(N_c) and discuss its application to lattice QCD.Comment: 6 pages, Lattice2002(theoretical), typo in Ref.[1] correcte

Direct observation of localization in the minority-spin-band electrons of magnetite below the Verwey temperature

Two-dimensional spin-uncompensated momentum density distributions, $\rho_{\rm s}^{2D}({\bf p})$s, were reconstructed in magnetite at 12K and 300K from several measured directional magnetic Compton profiles. Mechanical de-twinning was used to overcome severe twinning in the single crystal sample below the Verwey transition. The reconstructed $\rho_{\rm s}^{2D}({\bf p})$ in the first Brillouin zone changes from being negative at 300 K to positive at 12 K. This result provides the first clear evidence that electrons with low momenta in the minority spin bands in magnetite are localized below the Verwey transition temperature.Comment: 13 pages, 4 figures, accepted in Physical Review