Systematics of Charged Particle Production in Heavy-Ion Collisions with the PHOBOS Detector at RHIC

The multiplicity of charged particles produced in Au+Au collisions as a function of energy, centrality, rapidity and azimuthal angle has been measured with the PHOBOS detector at RHIC. These results contribute to our understanding of the initial state of heavy ion collisions and provide a means to compare basic features of particle production in nuclear collisions with more elementary systems.Comment: 4 pages, 4 figures (in eps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

A New Characterization of Fine Scale Diffusion on the Cell Membrane

We use a large single particle tracking data set to analyze the short time and small spatial scale motion of quantum dots labeling proteins in cell membranes. Our analysis focuses on the jumps which are the changes in the position of the quantum dots between frames in a movie of their motion. Previously we have shown that the directions of the jumps are uniformly distributed and the jump lengths can be characterized by a double power law distribution. Here we show that the jumps over a small number of time steps can be described by scalings of a {\em single} double power law distribution. This provides additional strong evidence that the double power law provides an accurate description of the fine scale motion. This more extensive analysis provides strong evidence that the double power law is a novel stable distribution for the motion. This analysis provides strong evidence that an earlier result that the motion can be modeled as diffusion in a space of fractional dimension roughly 3/2 is correct. The form of the power law distribution quantifies the excess of short jumps in the data and provides an accurate characterization of the fine scale diffusion and, in fact, this distribution gives an accurate description of the jump lengths up to a few hundred nanometers. Our results complement of the usual mean squared displacement analysis used to study diffusion at larger scales where the proteins are more likely to strongly interact with larger membrane structures.Comment: 18 pages, 7 figure

Extracting joint weak values with local, single-particle measurements

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure weakly in practice (for instance, in optics -- a common testing ground for this technique -- strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.Comment: 6 page

Quantum Nonlocality in Two-Photon Experiments at Berkeley

We review some of our experiments performed over the past few years on two-photon interference. These include a test of Bell's inequalities, a study of the complementarity principle, an application of EPR correlations for dispersion-free time-measurements, and an experiment to demonstrate the superluminal nature of the tunneling process. The nonlocal character of the quantum world is brought out clearly by these experiments. As we explain, however, quantum nonlocality is not inconsistent with Einstein causality.Comment: 16 pages including 24 figure

Nonlinear optics with less than one photon

We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch, and promises to be useful for a variety of nonlinear optical effects at the quantum level.Comment: 8 pages, 5 figure

Causality and Electromagnetic Transmissions Through Materials

There have been several experiments which hint at evidence for superluminal transport of electromagnetic energy through a material slab. On the theoretical side, it has appeared evident that acausal signals are indeed possible in quantum electrodynamics. However, it is unlikely that superluminal signals can be understood on the basis of a purely classical electrodynamic signals passing through a material. The classical and quantum theories represent quite different views, and it is the quantum view which may lead to violations of Einstein causality.Comment: Plain TeX, No figures, 5 page

On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page