On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

MODEL COMPARISON FOR ACOUSTIC SCATTERING BY A SPHERICAL AIR BUBBLE IN WATER

The oscillation of a bubble has many vibrational modes, contributing to different portions in acoustic scattering. Without approximations a priori, an hydrodynamic approach is applied to investigate acoustic scattering by a bubble in water, taking into account the heat exchange and viscosity. The scattering function is derived for a wide range of frequencies. Examples are shown to illustrate the thermal and viscous effects on sound scattering. Comparison is made with three existing models. While these models are known not to be applicable for high frequencies, it is shown here that even in the low-frequency region, there are also noticeable discrepancies between the exact solution and the three existing models with regard to the scattering properties such as the scattering cross-section, and the quality factor of resonant peaks. By numerical simulation, we claim that the discrepancies may be due to the incomplete consideration of the thermal exchange process in the previous models. The approach presented here is valid for any other fluid enclosure in liquids.     

Interference of spin splittings in magneto-oscillation phenomena in two-dimensional systems

The spin splitting caused by the terms linear in wavevector in the effective Hamiltonian containing can give rise to the new magneto-oscillation phenomena in two-dimensional systems. It is shown that the joint action of the spin-dependent contributions due to the heterostructure asymmetry and to the lack of inversion center in the bulk material suppresses beats that arise in the magneto-oscillation phenomena in the presence of the terms of only one of these types.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

Magnetic properties of oxygenated carbon nitride films from RF-discharge in an acetylene, nitrogen, and oxygen mixture environments

Properties of oxygenated carbon nitride films have attracted the attention of physics researchers due to their magnetic and physical properties, as well as for their usefulness in the industry. The free radicals were investigated using electron paramagnetic resonance applied in the study of spin concentration due to the different mechanism of preparation of carbon nitride films by RF-discharge with different kinds of plasma. Unpaired spin concentrations, in the order of 10²⁰ per cm³, were measured and their time recombination dependency was important in those films. The films were grown by plasma enhanced chemical vapor deposition using mixtures of hydrocarbons, N₂ and O₂ in different proportions.     

Computer simulation of selective absorption of radiation by the components of a light-scattering layer

A method of calculating the partial characteristics of radiation absorption by the components of light-scattering disperse layers is proposed. This method is based on statistical modeling (the Monte Carlo method). The absorptivities of photographic gelatin and silver bromide microcrystals and the corresponding distributions of the absorbed energy over the layer thickness are calculated using the example of an interaction between actinic radiation and silver halide photographic layers in the wavelength range λ=200–440 nm. The following structural parameters of the photographic layer are used in the calculation: the mean size of emulsion crystals d=0.5 μm; the polydispersity C _V =25%; the volume concentrations C _V =10, 20, and 30%; and the thickness of the emulsion layer H=10 μm.     

A comprehensive study of the long pulse Nd:YAG laser drilling of multi-layer carbon fibre composites

The results of an extensive experimental study of the free running Nd:YAG laser drilling of a multi-layer carbon fibre composite, where adjacent layers have differently orientated fibres, are reported. For holes drilled with the laser operating in fixed-Q mode at 1064 nm, parallel sections of blind holes illustrating discontinuities in the hole size along a given section direction will be shown to occur at the interface between adjacent layers. An explanation for this effect is proposed. Detailed single pulse drilling characteristics will be presented illustrating the exit hole diameter as a function of pulse energy and material thickness. These characteristics illustrate a ‘stable' drilling regime in which the exit hole diameters are least sensitive to changes in pulse energy or material thickness and a less ‘stable' regime in which they are more strongly dependent on these parameters. Drilling characteristics will be given for two different beam qualities, illustrating the greater drilling depth and reduced hole size achievable with an improved beam quality. Finally holes drilled through a 2 mm thick sample of material with multiple pulses are considered. Size distribution curves for entrance and exit holes will be presented. The total energy required (number of pulses × pulse energy) to drill through 2 mm thick material will be reported as a function of pulse energy in stationary air and argon atmospheres and in a partial vacuum, illustrating a threshold energy which is dependent upon the drilling atmosphere. The threshold energies will be discussed with reference to plasma formation and the reactivity of the drilling atmosphere.     

Mass transport in metals under intensive impulse reactions

An unusually high mobility of atoms under intensive impulse reactions is explained by the behavior of point defects at the shock wave front. It is shown that either a shock wave front or moving dislocations can capture the interstitials, or they can be thermally activated in the direction of the shock wave propagation.     

A method for computing the IR radiation of molecular gas jets in the volume approximation

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 3, pp. 478–484, September, 1991.     

Rb saturation spectroscopy with an optically narrowed FM diode laser

A fast-frequency modulated (FM) diode laser has been optically narrowed using the technique of resonant optical feedback, to provide linewidths in each FM mode of ≈ 200 kHz peak-to-peak. With a drive frequency of 50 MHz and modulation index of 0.2, the FM laser has been used for the first time to obtain Doppler-free FM spectra of the Rb D₁ line at 795 nm. The potential use of this system for laser frequency stabilisation is discussed.