Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Rhythmic inhibition allows neural networks to search for maximally consistent states

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena

Size of Fireballs Created in High Energy Lead-Lead Collisions as Inferred from Coulomb Distortions of Pion Spectra

We compute the Coulomb effects produced by an expanding, highly charged fireball on the momentum distribution of pions. We compare our results to data on Au+Au at 11.6 A GeV from E866 at the BNL AGS and to data on Pb+Pb at 158 A GeV from NA44 at the CERN SPS. We conclude that the distortion of the spectra at low transverse momentum and mid-rapidity can be explained in both experiments by the effect of the large amount of participating charge in the central rapidity region. By adjusting the fireball expansion velocity to match the average transverse momentum of protons, we find a best fit when the fireball radius is about 10 fm, as determined by the moment when the pions undergo their last scattering. This value is common to both the AGS and CERN experiments.Comment: Enlarged discussion, new references added, includes new analysis of pi-/pi+ at AGS energies. 12 pages 5 figures, uses LaTex and epsfi

The extent of strangeness in equilibration in quark-gluon plasma

The evolution and production of strangeness from chemically equilibrating and transversely expanding quark gluon plasma which may be formed in the wake of relativistic heavy ion collisions is studied with initial conditions obtained from the Self Screened Parton Cascade (SSPC) model. The extent of partonic equilibration increases almost linearly with the square of the initial energy density, which can then be scaled with number of participants.Comment: 4 pages including three figures, talk given at ICPAQGP'01, Jaipur, India, to appear in Pramana - Journal of Physics, Indian Academy of Scienc

Chemical equilibration of quarks and gluons at RHIC and LHC energies

We study chemical equilibration of quarks and gluons in central nuclear collisions at RHIC and LHC energies. The initial quark and gluon densities are taken from earlier studies as well as from recent perturbative QCD estimates and are then evolved via rate equations coupled to longitudinally boost-invariant fluid dynamics. We find that, for RHIC initial conditions, the lifetime of quark-gluon matter is too short in order for the quark and gluon number densities to chemically equilibrate prior to hadronization. In contrast, at LHC energies chemical equilibration is complete before the system hadronizes. Entropy production due to chemical equilibration can be as large as 30%.Comment: 30 pages (latex2e), 13 postscript figures, corrected one figure, further analysis performed, to be published in NP

Metal-insulator transitions: Influence of lattice structure, Jahn-Teller effect, and Hund's rule coupling

We study the influence of the lattice structure, the Jahn-Teller effect and the Hund's rule coupling on a metal-insulator transition in AnC60 (A= K, Rb). The difference in lattice structure favors A3C60 (fcc) being a metal and A4C60 (bct) being an insulator, and the coupling to Hg Jahn-Teller phonons favors A4C60 being nonmagnetic. The coupling to Hg (Ag) phonons decreases (increases) the value Uc of the Coulomb integral at which the metal-insulator transition occurs. There is an important partial cancellation between the Jahn-Teller effect and the Hund's rule coupling.Comment: 4 pages, RevTeX, 3 eps figure, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

Low Energy Analyzing Powers in Pion-Proton Elastic Scattering

Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.Comment: 15 pages, 4 figure

Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State

We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the compressibility sum rule and inconsistent with earlier work that did not account for consistency between the exchange-local-field and the disorder potential. We conclude that the thermodynamic density of states is finite, in spite of the vanishing tunneling density of states at the critical energy of the integer quantum Hall transition.Comment: 5 pages, 4 figures, minor revisions, published versio

Unified analysis of terminal-time control in classical and quantum systems

Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control for maximizing an objective is strongly affected by the possible existence of sub-optimal maxima. Within a unified framework under specified conditions, control objectives for maximizing at a terminal time physical observables of open classical and quantum systems are shown to be inherently free of sub-optimal maxima. This attractive feature is of central importance for enabling the discovery of controls in a seamless fashion in a wide range of phenomena transcending the quantum and classical regimes.Comment: 10 page

Integer quantum Hall effect of interacting electrons: dynamical scaling and critical conductivity

We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find numerical evidence for dynamical scaling with a dynamical critical exponent z=1 at the integer quantum Hall plateau transition in the lowest Landau level. Within the numerical accuracy of our data the conductivity at the transition and the anomalous diffusion exponent are given by the values for non-interacting electrons, independent of the strength of the interaction.Comment: Minor changes. Final version to be published in Phys. Rev. Lett. June 2