Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

An experiment to measure collisionless radial transport ofenergetic electrons confined by a dipole magnetic field

A new laboratory terrella has been constructed in order to study collisionless radial diffusion of particles trapped within a dipole magnetic field. Columbia's collisionless terrella experiment (CTX) aims to reproduce the process of wave-induced radial transport and does not try to simulate magnetospheric structure. The first experiment planned for CTX is the direct measurement of stochastic radial diffusion induced from wave-particle drift resonances. The motivation for the CTX experiment is described, and the procedures to be used to measure the intensity and spectrum of fluctuations generating chaos, the rate of radial transport, and the evolution of the density and pressure profiles are illustrated. Because of the success of similar experiments conducted earlier in a long thin magnetic mirror, these dipole experiments can be performed with a high degree of confidence. An example from these earlier experiments is presented     

Parametric modelling of Poisson-Gaussian random matrix ensembles

We analyse a scheme of transition from the Poissonian statistics for quantum levels to the Gaussian one of random matrix ensembles in the framework of level dynamics discussed by Yukawa. We propose a means of connecting these two limiting statistics by showing a result that Yukawa's parameter / of the exponential family can be efficiently replaced by the ratio <E>/<Q> which reflects directly a degree of the eigenvalue correlations of each sample matrix in the ensemble. On this basis, we discuss a correspondence between the level statistics of a generic quantum system and its classical regular/chaotic dynamics in terms of the semiclassical power spectrum and its second moment formulated by Feingold-Peres and Prosen-Robnik. We also discuss some limiting proceduresN (infinite limit of the matrix dimension) pertinent to the Gaussian ensembles, and remark about the possibility offractional power law of Brody's type.     

Kinetic investigation on carbamate formation from the reaction of carbon dioxide with amino acids in homogeneous aqueous solution

The kinetics of carbamate formation from the reaction of carbon dioxide with α‐amino acids in D₂O was first investigated by means of nuclear magnetic resonance spectroscopy. Potassium carbonate was used as the CO₂ source. For each amino acid, the maximum carbamate yield, the apparent rate constant for the carbamate formation k_app, and the rate constants for the formation k₁ and the breakdown k_?1 of the carbamate were estimated. Plots of log k₁ or log k_?1 versus pK_a of amino acids indicated that the formation rate k₁ increased with the basicity (pK_a) of amino acid, while the decomposition rate k_?1 decreased. A Br?nsted β value of 0.39 was obtained from the former plot, being in good agreement with the previously reported ones (0.26–0.43). The observed negative pK_a dependence of log k_?1 (Br?nsted α = 0.34) is reasonable, because the carbamate decomposition is acid‐catalyzed and the steady‐state concentration of H⁺ should be higher for weaker basic amines. The charge (σ) and the lone‐pair energy (E_N) at the nitrogen atom of the amino group were calculated. Although log k₁ correlated with σ and E_N, log k_?1 was unrelated with both of these parameters. Considering that the carbamate formation (k₁) is not only base‐catalyzed but should also be promoted by the nucleophilicity of the amino nitrogen, its correlation with σ and E_N in addition to pK_a is rational. The irrelevance of log k_?1 to σ and E_N is not surprising, because σ and E_N are not a direct measure of [H⁺] of the solution. Copyright © 2011 John Wiley & Sons, Ltd.     

Ruijsenaars' Commuting Difference Operators as Commuting Transfer Matrices

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation RLL=LLR, taking the trace of the L-operator gives a set of commuting difference operators. We show that for the above mentioned L-operator this approach gives Macdonald type operators with elliptic theta function coefficient, actually equivalent to Ruijsenaars' operators. The relationship between the difference L-operator and Krichever's Lax matrix is given, and an explicit formula for elliptic commuting differential operators is derived. We also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space. Received: 27 December 1995 / Accepted: 11 November 1996