Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.     

Glycoconjugated polymer 6. Synthesis of poly[styrene-<Emphasis Type="Italic">block</Emphasis>-(styrene-<Emphasis Type="Italic">graft</Emphasis>-amylose)] via potato phosphorylase-catalyzed polymerization

Summary The potato phosphorylase-catalyzed polymerization of α-D-glucose-1-phosphate (G-1-P) onto poly[styrene-block-(4-vinylbenzyl maltohexaoside)] (1) was performed at the molar ratios of [G-l-P]₀ and [maltohexaose]₀ of 35, 80, and 250. The product was found to be soluble in dimethyl sulfoxide, which was a good solvent for amylose, and showed the complex-formation with iodine, indicating that the product was assignable to poly[styrene-block-(styrene-graft-amylose)] (2). The quantitative analysis of the liberated phosphoric acid gave the average degree of polymerization o f the glucose unit (n) as 27, 5 1, and 180 for 2-I, 2-II, and 2-III, respectively. Received: 29 November 2002/Accepted: 22 December 2002 Correspondence to Toyoji Kakuchi     

Minimax estimation of deterministic parameters in linear models with a random model matrix

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix, with known second-order statistics. We first seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all parameter vectors whose (possibly weighted) norm is bounded above. We show that the minimax MSE estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax MSE estimator. Using these conditions, we derive closed-form expressions for the minimax MSE estimator in some special cases. We then demonstrate, through examples, that the minimax MSE estimator can improve the performance over both a Baysian approach and a least-squares method. We then consider the case in which the norm of the parameter vector is also bounded below. Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference between the MSE attainable using a linear estimator that does not know the parameter vector, and the optimal MSE attained using a linear estimator that knows the parameter vector. For analytical tractability, we restrict our attention to the scalar case and develop a closed-form expression for the minimax regret estimator.     

Second harmonic generation from a ferroelectric film

We derive an expression for transmittivity (T_SHG) of second harmonic generation (SHG) signals from a ferroelectric (FE) film. Intensities of up and down fields in the medium are investigated in relation to T_SHG. The derivations are made based on undepletion of input fields and nonlinear wave equation derived from the Maxwell equations. We present two cases: film without mirrors and with partial mirrors. Expressions for the newly derived nonlinear susceptibility coefficients of SHG for real crystal symmetry [J. Opt. Soc. Am. B 19 (2002) 2007] are used to get more realistic results. Variations in T_SHG with respect to film thickness are illustrated.     

1/f noise in large-area Hg<Subscript>1−x</Subscript>Cd<Subscript>x</Subscript>Te photodiodes

The 1/f noise in photovoltaic (PV) molecular-beam epitaxy (MBE)-grown Hg_1−xCd_xTe double-layer planar heterostructure (DLPH) large-area detectors is a critical noise component with the potential to limit sensitivity of the cross-track infrared sounder (CrIS) instrument. Therefore, an understanding of the origins and mechanisms of noise currents in these PV detectors is of great importance. Excess low-frequency noise has been measured on a number of 1000-μm-diameter active-area detectors of varying “quality” (i.e., having a wide range of I-V characteristics at 78 K). The 1/f noise was measured as a function of cut-off wavelength under illuminated conditions. For short-wave infrared (SWIR) detectors at 98 K, minimal 1/f noise was measured when the total current was dominated by diffusion with white noise spectral density in the mid-10⁻¹⁵A/Hz^1/2 range. For SWIR detectors dominated by other than diffusion current, the ratio, α, of the noise current in unit bandwidth i_n(f = 1 Hz, V_d = −60 mV, and Δf = 1 Hz) to dark current I_d(V_d = −60 mV) was α_SW-d = i_n/I_d ∼ 1 × 10⁻³. The SWIR detectors measured at 0 mV under illuminated conditions had median α_SW-P = i_n/I_ph ∼ 7 × 10⁻⁶. For mid-wave infrared (MWIR) detectors, α_MW-d = i_n/I_d ∼ 2 × 10⁻⁴, due to tunneling current contributions to the 1/f noise. Measurements on forty-nine 1000-μm-diameter MWIR detectors under illuminated conditions at 98 K and −60 mV bias resulted in α_MW-P = i_n/I_ph = 4.16 ± 1.69 × 10⁻⁶. A significant point to note is that the photo-induced noise spectra are nearly identical at 0 mV and 100 mV reverse bias, with a noise-current-to-photocurrent ratio, α_MW-P, in the mid 10⁻⁶ range. For long-wave infrared (LWIR) detectors measured at 78 K, the ratio, α_LW-d = i_n/I_d ∼ 6 × 10⁻⁶, for the best performers. The majority of the LWIR detectors exhibited α_LW-d on the order of 2 × 10⁻⁵. The photo-induced 1/f noise had α_LW-P = i_n/I_ph ∼ 5 × 10⁻⁶. The value of the noise-current-to-dark-current ratio, α appears to increase with increasing bandgap. It is not clear if this is due to different current mechanisms impacting 1/f noise performance. Measurements on detectors of different bandgaps are needed at temperatures where diffusion current is the dominant current. Excess low-frequency noise measurements made as a function of detector reverse bias indicate 1/f noise may result primarily from the dominant current mechanism at each particular bias. The 1/f noise was not a direct function of the applied bias.     

MULTICARRIER DS—CDMA WITH ADAPTIVE MODULATION AND POWER ALLOCATION

Adaptive modulation and power allocation is introduced into the multicarrier DSCDMA system to improve the system performance and bandwidth efficiency.First,the system design appropriate for adaptive modulation and power allocation is given,then the algorithm of adaptive modulation and power allocation is applied.Simulation results demonstrate great performance improvement compared with the fixed modulated one.     

Exchange-correlation errors at harmonic and anharmonic orders: the case of bulk Cu

As an aid towards improving the treatment of exchange and correlation effects in electronic structure calculations, it is desirable to have a clear picture of the errors introduced by currently popular approximate exchange-correlation functionals. We have performed ab initio density functional theory and density functional perturbation theory calculations to investigate the thermal properties of bulk Cu, using both the local density approximation (LDA) and the generalized gradient approximation (GGA). Thermal effects are treated within the quasiharmonic approximation. We find that the LDA and GGA errors for anharmonic quantities are an order of magnitude smaller than for harmonic quantities; we argue that this might be a general feature. We also obtain much closer agreement with experiment than earlier, more approximate calculations.     

The First Template‐Free Growth of Crystalline Silicon Microtubes

A simple template‐free high‐temperature evaporation method was developed for the growth of crystalline Si microtubes for the first time. As‐grown Si microtubes were characterized using X‐ray diffraction, scanning electron microscopy, transmission electron microscopy, and room‐temperature photoluminescence. The lengths of the Si tubes can reach several hundreds of micrometers; some of them have lengths on the order of millimeters. Each tube has a uniform outer diameter along its entire length, and the typical outer diameter is ≈ 2–3 μm. Most of the tubes have a wall thickness of ≈ 400–500 nm, though a considerable number of them exhibit a very thin wall thickness of ≈ 50 nm. Room‐temperature photoluminescence measurement shows the as‐synthesized Si microtubes have two strong emission peaks centered at ≈ 589 nm and ≈ 617 nm and a weak emission peak centered at ≈ 455 nm. A possible mechanism for the formation of these Si tubes is proposed. We believe that the present discovery of the crystalline Si microtubes will promote further experimental studies on their physical properties and smart applications.     

Electronic properties of magnetically doped nanotubes

Effect of doping of carbon nanotubes by magnetic transition metal atoms has been considered in this paper. In the case of semiconducting tubes, it was found that the system has zero magnetization, whereas in metallic tubes the valence electrons of the tube screen the magnetization of the dopants: the coupling to the tube is usually antiferromagnetic (except for Cr).