Phase Space Tomography of Classical and Nonclassical Vibrational States of Atoms in an Optical Lattice

Atoms trapped in optical lattice have long been a system of interest in the AMO community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to quantum information processing. Here we demonstrate for the first time complete determination of the quantum phase space distributions for an ensemble of $^{85}Rb$ atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.Comment: Submitted to Journal of Optics B: Quantum and Semiclassical Optics. Special issue in connection with the 9th International Conference on Squeezed States and Uncertainty Relations, to be held in Besancon, France, on 2-6 May 200

Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma

The hot nuclear matter created at the Relativistic Heavy Ion Collider (RHIC) has been characterized by near-perfect fluid behavior. We demonstrate that this stands in contradiction to the identification of QCD quasi-particles with the thermodynamic degrees of freedom in the early (fluid) stage of heavy ion collisions. The empirical observation of constituent quark ``$n_q$'' scaling of elliptic flow is juxtaposed with the lack of such scaling behavior in hydrodynamic fluid calculations followed by Cooper-Frye freeze-out to hadrons. A ``quasi-particle transport'' time stage after viscous effects break down the hydrodynamic fluid stage, but prior to hadronization, is proposed to reconcile these apparent contradictions. However, without a detailed understanding of the transitions between these stages, the ``$n_q$'' scaling is not a necessary consequence of this prescription. Also, if the duration of this stage is too short, it may not support well defined quasi-particles. By comparing and contrasting the coalescence of quarks into hadrons with the similar process of producing light nuclei from nucleons, it is shown that the observation of ``$n_{q}$'' scaling in the final state does not necessarily imply that the constituent degrees of freedom were the relevant ones in the initial state.Comment: 9 pages, 7 figures, Updated text and figure

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

Rank 3 permutation characters and maximal subgroups

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

Distinction of representations via Bruhat-Tits buildings of p-adic groups

Introductory and pedagogical treatmeant of the article : P. Broussous "Distinction of the Steinberg representation", with an appendix by Fran\c{c}ois Court\`es, IMRN 2014, no 11, 3140-3157. To appear in Proceedings of Chaire Jean Morlet, Dipendra Prasad, Volker Heiermann Ed. 2017. Contains modified and simplified proofs of loc. cit. This article is written in memory of Fran\c{c}ois Court\`es who passed away in september 2016.Comment: 33 pages, 4 figure

Hotter, Denser, Faster, Smaller...and Nearly-Perfect: What's the matter at RHIC?

The experimental and theoretical status of the ``near perfect fluid'' at RHIC is discussed. While the hydrodynamic paradigm for understanding collisions at RHIC is well-established, there remain many important open questions to address in order to understand its relevance and scope. It is also a crucial issue to understand how the early equilibration is achieved, requiring insight into the active degrees of freedom at early times.Comment: 10 Pages, 13 Figures, submitted to the proceedings of the Second Meeting of the APS Topical Group on Hadronic Physics, Nashville, TN, October 22-24, 200

System-size dependence

The final state in The final state in heavy-ion collisions has a higher degree of strangeness saturation than the one produced in collisions between elementary particles like p-p or p-$\bar{p}$. A systematic analysis of this phenomenon is made for C-C, Si-Si and Pb-Pb collisions at the CERN SPS collider and for $Au-Au$ collisions at RHIC and at AGS energies. Strangeness saturation is shown to increase smoothly with the number of participants at AGS, CERN and RHIC energies.Comment: 5 pages, 5 figures, presented at SQM2003 conferenc

Conditional probabilities in quantum theory, and the tunneling time controversy

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts

Traveling Wave Fronts and Localized Traveling Wave Convection in Binary Fluid Mixtures

Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated from below. A finite-difference method is used to solve the full hydrodynamic field equations in a vertical cross section of the layer perpendicular to the convection roll axes. Results are presented for ethanol-water parameters with several strongly negative separation ratios where TW solutions bifurcate subcritically. Fronts and LTWs are compared with each other and similarities and differences are elucidated. Phase propagation out of the quiescent fluid into the convective structure entails a unique selection of the latter while fronts and interfaces where the phase moves into the quiescent state behave differently. Interpretations of various experimental observations are suggested.Comment: 46 pages, 11 figures. Accepted for publication in Phys. Rev.

Conjugacy theorems for loop reductive group schemes and Lie algebras

The conjugacy of split Cartan subalgebras in the finite dimensional simple case (Chevalley) and in the symmetrizable Kac-Moody case (Peterson-Kac) are fundamental results of the theory of Lie algebras. Among the Kac-Moody Lie algebras the affine algebras stand out. This paper deals with the problem of conjugacy for a class of algebras --extended affine Lie algebras-- that are in a precise sense higher nullity analogues of the affine algebras. Unlike the methods used by Peterson-Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of reductive group schemes developed by Demazure and Grothendieck, and on the work of J. Tits on buildingsComment: Publi\'e dans Bulletin of Mathematical Sciences 4 (2014), 281-32