Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings are related through the single-valued map `sv'. This relation can be traced back to the underlying moduli-space integrals over punctured Riemann surfaces of genus zero. The sphere integrals $J$ in closed-string amplitudes and the disk integrals $Z$ in open-string amplitudes are shown to obey $J = {\rm sv} \, Z$.

Oliver Schlotterer Oliver Schnetz

The intense UV radiation from a highly luminous QSO should excite fluorescent Ly-alpha emission from any nearby neutral hydrogen clouds. We present a very deep narrow-band search for such emission near the z=2.168 quasar PKS 0424-131, obtained with the Taurus Tunable Filter on the Anglo-Australian Telescope. By working in the UV, at high spectral resolution and by using charge shuffling, we have been able to reach surface brightness limits as faint as 4.7E-19 erg/cm^2/s/arcsec^2. No fluorescent Ly-alpha emission is seen, whereas QSO absorption-line statistics suggest that we should have seen ~6 clouds, unless the clouds are larger than ~ 100 kpc in size. Furthermore, we do not even see the normal population of Ly-alpha emitting galaxies found by other surveys at this redshift. This is very different fromobservations of high redshift radio galaxies, which seem to be surrounded by clusters of Ly-alpha emitters. We tentatively conclude that there is a deficit of neutral hydrogen close to this quasar, perhaps due to the photo-evaporation of nearby dwarf galaxies.

Paul J. Francis Joss Bland-Hawthorn

We consider large time behavior of typical paths under the Anderson polymer measure. If $P$ is the measure induced by rate $\kappa,$ simple, symmetric random walk on $Z^d$ started at $x,$ this measure is defined as $$ d\mu(X)={Z^{-1} \exp\{\beta\int_0^T dW_{X(s)}(s)\}dP(X) $$ where $\{W_x:x\in Z^d\}$ is a field of $iid$ standard, one-dimensional Brownian motions, $\beta>0, \kappa>0$ and $Z$ the normalizing constant. We establish that the polymer measure gives a macroscopic mass to a small neighborhood of a typical path as $T \to \infty$, for parameter values outside the perturbative regime of the random walk, giving a pathwise approach to polymer localization, in contrast with existing results. The localization becomes complete as $\frac{\beta^2}{\kappa}\to\infty$ in the sense that the mass grows to 1. The proof makes use of the overlap between two independent samples drawn under the Gibbs measure $\mu$, which can be estimated by the integration by parts formula for the Gaussian environment. Conditioning this measure on the number of jumps, we obtain a canonical measure which already shows scaling properties, thermodynamic limits, and decoupling of the parameters.

Francis Comets Michael Cranston

The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can be equivalently defined on the original sequence and its $z$-transform. In particular, the z-transform method focuses on asymptotic behaviors and allows the use of Taylor expansions. We present a sequence of results of increasing significance and difficulty for linear models and optimization algorithms, demonstrating the effectiveness and versatility of the z-transform method in deriving new asymptotic results. Starting from the simplest gradient descent iterations in an infinite-dimensional Hilbert space, we show how the spectral dimension characterizes the convergence behavior. We then extend the analysis to Nesterov acceleration, averaging techniques, and stochastic gradient descent.

Francis Bach

We present a detailed study of a rich galaxy cluster at z=2.38. We demonstrate that this cluster contains large overdensities of damped Ly-alpha absorption lines, of Ly-alpha emitting galaxies and of extremely red objects. The overdensity of extremely red objects in this field demonstrates that many are high z galaxies. The huge overdensities we measure for these three classes of object are much larger than the mass overdensities of typical clusters at this redshift, as predicted by CDM and related models. We suggest therefore that the distribution of damped Ly-alpha absorption line systems, of Ly-alpha emitting galaxies and of extremely red objects are all very strongly biassed, and that somehow a small overdensity of mass has increased the fraction of baryons in collapsed objects, in the volume occupied by the cluster, to close to unity (a factor of ~10 increase). We speculate that some unknown physical process, acting on the volume occupied by our cluster, caused the normally diffuse ionised inter-galactic medium to coalesce into small (< 10^8 Solar masses) blobs of neutral hydrogen, which produce the Ly-alpha absorption-lines. Star formation occurred within these blobs at z>5, enriching them with metals and producing stars, which after several mergers and ~ 0.5 Gyr of passive evolution form the extremely red objects. The Ly-alpha emitting galaxies are probably AGN, triggered perhaps by mergers of the small blobs.

Paul J. Francis Bruce E. Woodgate Anthony C. Danks

We propose an improved composite-boson theory of quantum Hall ferromagnets, where the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. In this scheme skyrmions appear merely as generic excitations confined in the lowest Landau level. We evaluate the excitation energy of one skyrmion. Our theoretical estimation accounts for the activation-energy data due to Schmeller et al. remarkably well.

Z. F. Ezawa

An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.

Z. F. Ezawa

We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $\nu=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $\nu =1$ and discovered at $\nu =2$. In particular, three different $\nu =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.

A. Sawada Z. F. Ezawa H. Ohno Y. Horikoshi A. Urayama Y. Ohno S. Kishimoto F. Matsukura N. Kumada

We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$\nu =2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.

Z. F. Ezawa

An improved composite-boson theory of quantum Hall ferromagnets is proposed. It is tightly related with the microscopic wave-function theory. The characteristic feature is that the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. It presents a powerful tool to analyze excited states within the \LLLd. Excitations include a Goldstone mode and nonlocal topological solitons. Solitons are vortices and Skyrmions carrying the U(1) and SU(2) topological charges, respectively. Their classical configurations are derived from their microscopic wave functions. The activation energy of one Skyrmion is estimated, which explains experimental data remarkably well.

Z. F. Ezawa K. Sasaki