Nodal domains of Maass forms I

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the $L^2$-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.Comment: To appear in GAF

Nuclear dependence coefficient α(A,qT)\alpha(A,q_T) for the Drell-Yan and J/ψ\psi production

Define the nuclear dependence coefficient $\alpha(A,q_T)$ in terms of ratio of transverse momentum spectrum in hadron-nucleus and in hadron-nucleon collisions: $\frac{d\sigma^{hA}}{dq_T^2}/ \frac{d\sigma^{hN}}{dq_T^2}\equiv A^{\alpha(A,q_T)}$. We argue that in small $q_T$ region, the $\alpha(A,q_T)$ for the Drell-Yan and J/$\psi$ production is given by a universal function:\ $a+b q_T^2$, where parameters a and b are completely determined by either calculable quantities or independently measurable physical observables. We demonstrate that this universal function $\alpha(A,q_T)$ is insensitive to the A for normal nuclear targets. For a color deconfined nuclear medium, the $\alpha(A,q_T)$ becomes strongly dependent on the A. We also show that our $\alpha(A,q_T)$ for the Drell-Yan process is naturally linked to perturbatively calculated $\alpha(A,q_T)$ at large $q_T$ without any free parameters, and the $\alpha(A,q_T)$ is consistent with E772 data for all $q_T$.Comment: latex, 28 pages, 10 figures, updated two figures, and add more discussion

Coherent spin valve phenomena and electrical spin injection in ferromagnetic/semiconductor/ferromagnetic junctions

Coherent quantum transport in ferromagnetic/ semiconductor/ ferromagnetic junctions is studied theoretically within the Landauer framework of ballistic transport. We show that quantum coherence can have unexpected implications for spin injection and that some intuitive spintronic concepts which are founded in semi-classical physics no longer apply: A quantum spin-valve (QSV) effect occurs even in the absence of a net spin polarized current flowing through the device, unlike in the classical regime. The converse effect also arises, i.e. a zero spin-valve signal for a non-vanishing spin-current. We introduce new criteria useful for analyzing quantum and classical spin transport phenomena and the relationships between them. The effects on QSV behavior of spin-dependent electron transmission at the interfaces, interface Schottky barriers, Rashba spin-orbit coupling and temperature, are systematically investigated. While the signature of the QSV is found to be sensitive to temperature, interestingly, that of its converse is not. We argue that the QSV phenomenon can have important implications for the interpretation of spin-injection in quantum spintronic experiments with spin-valve geometries.Comment: 15 pages including 11 figures. To appear in PR

Spin relaxation: From 2D to 1D

In inversion asymmetric semiconductors, spin-orbit interactions give rise to very effective relaxation mechanisms of the electron spin. Recent work, based on the dimensionally constrained D'yakonov Perel' mechanism, describes increasing electron-spin relaxation times for two-dimensional conducting layers with decreasing channel width. The slow-down of the spin relaxation can be understood as a precursor of the one-dimensional limit

Atomic X-ray Spectroscopy of Accreting Black Holes

Current astrophysical research suggests that the most persistently luminous objects in the Universe are powered by the flow of matter through accretion disks onto black holes. Accretion disk systems are observed to emit copious radiation across the electromagnetic spectrum, each energy band providing access to rather distinct regimes of physical conditions and geometric scale. X-ray emission probes the innermost regions of the accretion disk, where relativistic effects prevail. While this has been known for decades, it also has been acknowledged that inferring physical conditions in the relativistic regime from the behavior of the X-ray continuum is problematic and not satisfactorily constraining. With the discovery in the 1990s of iron X-ray lines bearing signatures of relativistic distortion came the hope that such emission would more firmly constrain models of disk accretion near black holes, as well as provide observational criteria by which to test general relativity in the strong field limit. Here we provide an introduction to this phenomenon. While the presentation is intended to be primarily tutorial in nature, we aim also to acquaint the reader with trends in current research. To achieve these ends, we present the basic applications of general relativity that pertain to X-ray spectroscopic observations of black hole accretion disk systems, focusing on the Schwarzschild and Kerr solutions to the Einstein field equations. To this we add treatments of the fundamental concepts associated with the theoretical and modeling aspects of accretion disks, as well as relevant topics from observational and theoretical X-ray spectroscopy.Comment: 63 pages, 21 figures, Einstein Centennial Review Article, Canadian Journal of Physics, in pres

Thermodynamic Measurements in a Strongly Interacting Fermi Gas

We conduct a series of measurements on the thermodynamic properties of an optically-trapped strongly interacting Fermi gas, including the energy $E$, entropy $S$, and sound velocity $c$. Our model-independent measurements of $E$ and $S$ enable a precision study of the finite temperature thermodynamics. The $E(S)$ data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation $T=\partial E/\partial S$ by parameterizing the $E(S)$ data. Our $E(S)$ data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes. This enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation. Our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our $E(S)$ data. The results are in very good agreement with recent predictions. Finally, using universal thermodynamic relations, we estimate the chemical potential and heat capacity of the trapped gas from the $E(S)$ data.Comment: 29 pages, 12 figures. To appear in JLTP online, and in the January, 2009 volum

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.

A Measurement of Psi(2S) Resonance Parameters

Cross sections for e+e- to hadons, pi+pi- J/Psi, and mu+mu- have been measured in the vicinity of the Psi(2S) resonance using the BESII detector operated at the BEPC. The Psi(2S) total width; partial widths to hadrons, pi+pi- J/Psi, muons; and corresponding branching fractions have been determined to be Gamma(total)= (264+-27) keV; Gamma(hadron)= (258+-26) keV, Gamma(mu)= (2.44+-0.21) keV, and Gamma(pi+pi- J/Psi)= (85+-8.7) keV; and Br(hadron)= (97.79+-0.15)%, Br(pi+pi- J/Psi)= (32+-1.4)%, Br(mu)= (0.93+-0.08)%, respectively.Comment: 8 pages, 6 figure

\psi(2S) Decays into \J plus Two Photons

Using \gamma \gamma J/\psi, J/\psi \ra e^+ e^- and $\mu^+ \mu^-$ events from a sample of $14.0\times 10^6$ \psip decays collected with the BESII detector, the branching fractions for \psip\ra \pi^0\J, \eta\J, and \psi(2S)\ar\gamma\chi_{c1},\gamma\chi_{c2}\ar\gamma\gamma\jpsi are measured to be B(\psip\ra \pi^0\J) = (1.43\pm0.14\pm0.13)\times 10^{-3}, B(\psip\ra \eta\J) = (2.98\pm0.09\pm0.23)%, B(\psi(2S)\ar\gamma\chi_{c1}\ar\gamma\gamma\jpsi) = (2.81\pm0.05\pm 0.23)%, and B(\psi(2S)\ar\gamma\chi_{c2}\ar\gamma\gamma\jpsi) = (1.62\pm0.04\pm 0.12)%.Comment: 7 pages, 6 figures. submitted to Phys. Rev.