Researches on aromatic heterocyclic compounds III. The aromatic character of piazthiol

The PMR spectra of piazthiol, which is benzo[1,2-c]-[1,2,5]-thiodiazole, and of its- and-nitro, chloro, methyl and amino derivatives are investigated. The effects of these substituents on the chemical shift is in qualitative agreement with the like effects in the benzene series. The parameters of the corresponding PMR spectra are greatly dependent on the electrophilic action of the heterocyclic ring. It is shown that there is conjugation in the thiadiazole ring, although, however, it is much weakened compared with that existing in the benzene ring.For Part II see [10].The authors thank V. F. Bystrov for discussions, and for making the double resonance measurements with-methylpiazthiol in a JNM-C-60 spectrometer.     

The Lorentz Integral Transform and its Inversion

The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due to a historical misconception. In this connection standard regularization procedures for the solution of the integral transform problem are presented. In particular a recent one is considered in detail and critical comments on it are provided. In addition a general remark concerning the concept of the Lorentz integral transform as a method with a controlled resolution is made.     

Electrodynamics of metallic photonic crystals and the problem of left-handed materials

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence for such waves has been obtained recently by experiments and computations. The cutoff frequency of these waves, omega(0), is studied. An analytical expression for the permittivity epsilon is obtained and shown to be negative below omega(0). If the crystal is embedded into a medium with a negative mu, there are no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.     

Orbital mechanisms of electron-spin manipulation by an electric field

A theory of spin manipulation of quasi-two-dimensional (2D) electrons by a time-dependent gate voltage applied to a quantum well is developed. The Dresselhaus and Rashba spin-orbit coupling mechanisms are shown to be rather efficient for this purpose. The spin response to a perpendicular-to-plane electric field is due to a deviation from the strict 2D limit and is controlled by the ratios of the spin, cyclotron, and confinement frequencies. The dependence of this response on the magnetic field direction is indicative of the strengths of the competing spin-orbit coupling mechanisms.     

New class of magnetoresistance oscillations: interaction of a two-dimensional electron gas with leaky interface phonons

We report on a new class of magnetoresistance oscillations observed in a high-mobility two-dimensional electron gas (2DEG) in GaAs-Al(x)Ga(1--x)As heterostructures. Appearing in a weak magnetic field ( B < 0.3 T) and only in a narrow temperature range ( 2 K < T < 9 K), these oscillations are periodic in 1/B with a frequency proportional to the electron Fermi wave vector, k(F). We interpret the effect as a magnetophonon resonance of the 2DEG with leaky interface-acoustic phonon modes carrying a wave vector q = 2k(F). Calculations show a few branches of such modes existing on the GaAs-Al(x)Ga(1--)xAs interface, and their velocities are in quantitative agreement with the observation.     

A method for solving reaction and bound-state few-body problems: A > 3

A method for solving the few-body problems is described, which is based on the expansion in a small parameter: ratio of the potential energy to the kinetic energy for the states with the hyperspherical numbers K exceeding some value K ₀. The initial problem is reduced to that with modified dynamics in the subspace with K ≤ K ₀ without expansion in the basis functions at K > K ₀.