LSD and AMAZE: the mass-metallicity relation at z>3

We present the first results on galaxy metallicity evolution at z>3 from two projects, LSD (Lyman-break galaxies Stellar populations and Dynamics) and AMAZE (Assessing the Mass Abundance redshift Evolution). These projects use deep near-infrared spectroscopic observations of a sample of ~40 LBGs to estimate the gas-phase metallicity from the emission lines. We derive the mass-metallicity relation at z$>$3 and compare it with the same relation at lower redshift. Strong evolution from z=0 and z=2 to z=3 is observed, and this finding puts strong constrains on the models of galaxy evolution. These preliminary results show that the effective oxygen yields does not increase with stellar mass, implying that the simple outflow model does not apply at z>3.Comment: 5 pages, to appear in the IAUS 255 conference proceedings: "Low-Metallicity Star Formation: from the First Stars to Dwarf Galaxies", L.K. Hunt, S. Madden and R. Schneider ed

Eigenvalue statistics of the real Ginibre ensemble

The real Ginibre ensemble consists of random $N \times N$ matrices formed from i.i.d. standard Gaussian entries. By using the method of skew orthogonal polynomials, the general $n$-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as $n \times n$ Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis of biological webs.Comment: 4 pages, to appear PR

Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the GOE (Gaussian Orthogonal Ensemble) class to the GSE class.Comment: 25 pages, 2 figure

Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction

We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation is experimentally realizable when the spin-orbit interaction is controlled in a conductor by applying an electric field. We utilize a semiclassical approach which has recently been developed. In this approach, the non-Abelian nature of the spin diffusion along a classical trajectory plays a crucial role. New analytical expressions with one crossover parameter are semiclassically derived for the average conductance, conductance variance and shot noise. Moreover numerical results on a random matrix model describing the crossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (Gaussian Symplectic Ensemble) are compared with the semiclassical expressions.Comment: 13 pages, 7 figure

Is there any evidence that ionised outflows quench star formation in type 1 quasars at z<1?

The aim of this paper is to test the basic model of negative AGN feedback. According to this model, once the central black hole accretes at the Eddington limit and reaches a certain critical mass, AGN driven outflows blow out gas, suppressing star formation in the host galaxy and self-regulating black hole growth. We consider a sample of 224 quasars selected from the SDSS at z<1 observed in the infrared band by Herschel. We evaluate the star formation rate in relation to several outflow signatures traced by the [OIII]4959,5007 and [OII]3726,3729 emission lines in about half of the sample with high quality spectra. Most of the quasars show asymmetric and broad wings in [OIII], which we interpret as outflow signatures. We separate the quasars in two groups, ``weakly'' and ``strongly'' outflowing, using three different criteria. When we compare the mean star formation rate in five redshift bins in the two groups, we find that the SFRs are comparable or slightly larger in the strongly outflowing quasars. We estimate the stellar mass from SED fitting and the quasars are distributed along the star formation main sequence, although with a large scatter. The scatter from this relation is uncorrelated with respect to the kinematic properties of the outflow. Moreover, for quasars dominated in the infrared by starburst or by AGN emission, we do not find any correlation between the star formation rate and the velocity of the outflow, a trend previously reported in the literature for pure starburst galaxies. We conclude that the basic AGN negative feedback scenario seems not to agree with our results. Although we use a large sample of quasars, we did not find any evidence that the star formation rate is suppressed in the presence of AGN driven outflows on large scale. A possibility is that feedback is effective over much longer timescales than those of single episodes of quasar activity.Comment: 18 pages, new version that implements the suggestions of the referee and matches the AA published versio

Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous noncolliding systems of the Bessel processes and a two-parameter family of temporally inhomogeneous noncolliding systems of Yor's generalized meanders and show that all of the ten classes of eigenvalue statistics in the Altland-Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems. As a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process, a stochastic-calculus proof of a version of the Harish-Chandra (Itzykson-Zuber) formula of integral over unitary group is established.Comment: LaTeX, 27 pages, 4 figures, v3: Minor corrections made for publication in J. Math. Phy

Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model

We consider a quantum moany-body problem in one-dimension described by a Jastrow type, characterized by an exponent $\lambda$ and a parameter $\gamma$. We show that with increasing $\gamma$, the Fermi Liquid state ($\gamma=0)$ crosses over to non-Fermi liquid states, characterized by effective "temperature".Comment: 8pp. late

An Intermediate-band imaging survey for high-redshift Lyman Alpha Emitters: The Mahoroba-11

We present results of our intermediate-band optical imaging survey for high-$z$ Ly$\alpha$ emitters (LAEs) using the prime focus camera, Suprime-Cam, on the 8.2m Subaru Telescope. In our survey, we use eleven filters; four broad-band filters ($B$, $R_{\rm c}$, $i^\prime$, and $z^\prime$) and seven intermediate-band filters covering from 500 nm to 720 nm; we call this imaging program as the Mahoroba-11. The seven intermediate-band filters are selected from the IA filter series that is the Suprime-Cam intermediate-band filter system whose spectral resolution is $R = 23$. Our survey has been made in a $34^\prime \times 27^\prime$ sky area in the Subaru XMM Newton Deep Survey field. We have found 409 IA-excess objects that provide us a large photometric sample of strong emission-line objects. Applying the photometric redshift method to this sample, we obtained a new sample of 198 LAE candidates at $3 < z < 5$. We found that there is no evidence for evolution of the number density and the star formation rate density for LAEs with $\log L({\rm Ly}\alpha) ({\rm erg s^{-1}}) > 42.67$ between $z \sim 3$ and 5.Comment: 46 pages, 15 figures, PASJ, Vol.57, No.6, in pres

Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio

Functional central limit theorems for vicious walkers

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publicatio