Recent advances in terahertz imaging

We review recent progress in the field of terahertz “T-ray” imaging. This relatively new imaging technique, based on terahertz time-domain spectroscopy, has the potential to be the first portable far-infrared imaging spectrometer. We give several examples which illustrate the possible applications of this technology, using both the amplitude and phase information contained in the THz waveforms. We describe the latest results in tomographic imaging, in which waveforms reflected from an object can be used to form a three-dimensional representation. Advanced signal processing tools are exploited for the purposes of extracting tomographic results, including spectroscopic information about each reflecting layer of a sample. We also describe the application of optical near-field techniques to the THz imaging system. Substantial improvements in the spatial resolution are demonstrated. Received: 29 January 1999 / Published online: 7 April 1999     

Near Best Tree Approximation

Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure. This makes their positions easy to encode. Previous work [4,6] has established upper bounds for the error of tree approximation for certain (Besov) classes of functions. This paper, in contrast, studies tree approximation of individual functions with the aim of characterizing those functions with a prescribed approximation error. We accomplish this in the case that the approximation error is measured in L ₂, or in the case p2, in the Besov spaces B _p ⁰(L _p ), which are close to (but not the same as) L _p . Our characterization of functions with a prescribed approximation order in these cases is given in terms of a certain maximal function applied to the wavelet coefficients.     

RESTRICTED LIE ALGEBRAS WITH MAXIMAL 0-PIM

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p ^MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable.     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

Temperature hysteretic effect and its influence on colossal magnetoresistance of La0.33Nd0.33Ca0.33MnO3

Electrical resistance (R) measurements of a bulk La_0.33Nd_0.33Ca_0.33MnO₃ perovskite in magnetic fields up to 40 kOe have revealed anomalous temperature hysteretic effects both in 0 Oe and 20 kOe magnetic fields. The sharp peak observed in the R vs. T plot indicates the occurrence of metal-to-insulator (M-I) transition at a temperature of T _MI=110 K and 140 K, for cooling and warming paths, respectively. An applied magnetic field of 20 kOe reduces the resistance and shifts T _MI to 160 K and 185 K for cooling and warming, respectively. We have observed a much higher resistance in the cooling path than in the warming path leading to the hysteretic resistance ratio (R _cool/R _warm) of 200 at 110 K and 1.8 at 160 K for 0 Oe and 20 kOe, respectively. Record values of colossal magnetoresistance (CMR) have been achieved. The CMR value reaches nearly 99% in the temperature ranges of 90 K to 140 K and 90 K to 170 K for 20 kOe and 40 kOe magnetic fields in the cooling mode, respectively. The observed unusual behavior is attributed to the co-existence of La-rich and Nd-rich domains assumed to be distributed randomly in the compound.     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.