Infinite order symmetries for two-dimensional separable Schrödinger equations

Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates

Superintegrability in three-dimensional Euclidean space

Potentials for which the corresponding Schrödinger equation is maximally superintegrable in three-dimensional Euclidean space are studied. The quadratic algebra which is associated with each of these potentials is constructed and the bound state wave functions are computed in the separable coordinates

Meson exchange currents in electromagnetic one-nucleon emission

The role of meson exchange currents (MEC) in electron- and photon-induced one-nucleon emission processes is studied in a nonrelativistic model including correlations and final state interactions. The nuclear current is the sum of a one-body and of a two-body part. The two-body current includes pion seagull, pion-in-flight and the isobar current contributions. Numerical results are presented for the exclusive 16O(e,e'p)15N and 16O(\gamma,p)15N reactions. MEC effects are in general rather small in (e,e'p), while in (\gamma,p) they are always large and important to obtain a consistent description of (e,e'p) and (\gamma,p) data, with the same spectroscopic factors. The calculated (\gamma,p) cross sections are sensitive to short-range correlations at high values of the recoil momentum, where MEC effects are larger and overwhelm the contribution of correlations.Comment: 9 pages, 6 figure

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Narrative inquiry into (re)imagining alternative schools: a case study of Kevin Gonzales.

Although there are many alternative schools that strive for the successful education for their students, negative images of alternative schools persist. While some alternative schools are viewed as “idealistic havens,” many are viewed as “dumping grounds,” or “juvenile detention centers.” Employing narrative inquiry, this article interrogates how a student, Kevin Gonzales, experiences his alternative education and raises questions about the role of alternative schools. Kevin Gonzales’s story is presented in a literary form of biographical journal to provide a “metaphoric loft” that helps us imagine other students like Kevin. This, in turn, provokes us to examine our current educational practice, and to (re)imagine ways in which alternative education can provide the best possible educational experiences for disenfranchised students who are increasingly underserved by the public education system

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding

Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at sNN=200\sqrt{s_{NN}} = 200 GeV

Identified mid-rapidity particle spectra of $\pi^{\pm}$, $K^{\pm}$, and $p(\bar{p})$ from 200 GeV p+p and d+Au collisions are reported. A time-of-flight detector based on multi-gap resistive plate chamber technology is used for particle identification. The particle-species dependence of the Cronin effect is observed to be significantly smaller than that at lower energies. The ratio of the nuclear modification factor ($R_{dAu}$) between protons $(p+\bar{p})$ and charged hadrons ($h$) in the transverse momentum range $1.2<{p_{T}}<3.0$ GeV/c is measured to be $1.19\pm0.05$(stat)$\pm0.03$(syst) in minimum-bias collisions and shows little centrality dependence. The yield ratio of $(p+\bar{p})/h$ in minimum-bias d+Au collisions is found to be a factor of 2 lower than that in Au+Au collisions, indicating that the Cronin effect alone is not enough to account for the relative baryon enhancement observed in heavy ion collisions at RHIC.Comment: 6 pages, 4 figures, 1 table. We extended the pion spectra from transverse momentum 1.8 GeV/c to 3. GeV/

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

The energy dependence of ptp_t angular correlations inferred from mean-ptp_{t} fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure suggests that the principal source of $p_t$ correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related fluctuations near 10 GeV.Comment: 10 pages, 4 figure