Positive definite functions on the Heisenberg group

Work supported in part by the NSF     

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC ² norm, then a uniqueC ¹ solution to this system is shown to exist on all of spacetime.Research supported in part by NSF DMS 85-20662 and NSF DMS 84-20957     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.     

On non-Fermi liquid quantum critical points in heavy fermion metals

Heavy electron metals on the verge of a quantum phase transition to magnetism show a number of unusual non-Fermi liquid properties which are poorly understood. This article discusses in a general way various theoretical aspects of this phase transition with an eye toward understanding the non-Fermi liquid phenomena. We suggest that the non-Fermi liquid quantum critical state may have a sharp Fermi surface with power law quasiparticles but with a volume not set by the usual Luttinger rule. We also discuss the possibility that the electronic structure change associated with the possible Fermi surface reconstruction may diverge at a different time/length scale from that associated with magnetic phenomena.     

Anisotropy of two-photon absorption in gallium selenide at 1064 nm

The Bridgman method is used to grow single crystals of ε-GaSe. The two-photon absorption (TPA) coefficient β was measured for especially un-doped crystals at room temperature for the ordinary o-ray (β_⊥) and extraordinary e-ray (β_∥) using single-wavelength excitation by a Nd:YVO₄ laser at 1.064 μm with a pulse duration of 10 ps and a repetition rate of 81 MHz. No large anisotropy was observed for the TPA coefficients between the two geometries. The TPA coefficients were found to be β_⊥ = 1.07 × 10⁻⁹ cm/W and β_∥ = 1.88 × 10⁻⁹ cm/W. It was found that doping slightly increases the TPA coefficient. The value of the TPA for crystals doped with 0.5 at.% of Tl is β_⊥ = 7.56 × 10⁻⁹ cm/W.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

CsI(Tl)晶体中反冲Cs和I核Quenching?Factor的测量

许多实验对用CsI(Tl)闪烁晶体作为探测器来寻找和探测暗物质的可行性进行了研究.本工作利用8MeV单能中子轰击CsI(Tl)晶体探测器来研究Cs核和I核的QuenchingFactor.在数据处理中,运用脉冲形状甄别(PSD)方法来分辨反冲核信号和本底信号.实验结果表明,在7keV到132keV的能区中,Quench ingFactor随着反冲核能量的减少而增加.在探测暗物质的实验中,这一性质对于CsI(Tl)晶体探测器获得较低的能量阈值是很有利的.     

Investigations of Solid State Dynamics at the NRSSR Beamline at PETRA II. An Overview

The present status of the new nuclear resonance beamline PETRA 1 at HASYLAB, DESY, Hamburg is described. Besides an overview of the experimental setup some examples of recent experiments are given. Those cover the main applications, i.e., inelastic scattering from iron alloys and quasielastic scattering from glass-forming liquids. This revised version was published online in August 2006 with corrections to the Cover Date.     

Observation of dielectronic satellites in the K-spectrum of argon ions in plasma produced by femtosecond laser pulses

The satellite structure of 1s2p ^1,3 P ₁-1s ²¹ S ₀ lines of the He-like argon ion in plasma produced by a 45-fs laser pulse in a gas-jet cluster target is measured with a high spectral resolution. Radiation transitions 2p → 1s from autoionizing states (AISs) are detected for ions ranging from Li-like to F-like. The spectrum observed is theoretically simulated with the use of the spectroscopic data for the AISs of multicharged ions obtained within the multiconfiguration relativistic Hartree-Fock method. Good agreement with experimental data is obtained when the main population channels of these states are taken into account for typical values of cluster-target plasma parameters.