NLS-tupe equations in 2+1 dimensions: New type of solutions and non-isospectral problems

Integrable systems of NLS type in 2+1 dimensions are studied in three ways: their special solutions by Lie point symmetries, breaking-solutions by the ISM, as well as the non-isospectral problems.Department of Mathematics, Statistics and Computing Science, University of New England, Armidale N.S.W. 2351, Australia. E-mail: zhuhan@neumann.une.edu.au, xhe@metz.une.edu.au Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 382–389, June, 1994.     

On approximation of functions in terms of Φ-variation

Получен аналог теоре мы Джексона о приближ ении полиномами в метрике Ф-вариации; для некото рых классов функций (в ыпуклых, конечной вариации, с заданным модулем неп рерывности) установл ено соотношение типа сла бой эквивалентности, которое связывает ме жду собой рациональн ые аппроксимации, в этой и равномерной метриках Даны оценкиε-энтропи и в метрике Ф-вариации классов функций с заданным мо дулем Ф-абсолютной непреры вности и с заданным мо дулем непрерывности.     

Brownian motion with restoring drift: The petit and micro-canonical ensembles

Letf(Q) be odd and positive near +∞. Then the non-linear wave equation ?² Q/?t ²??² Q/?x ²?f(Q)=0, considered on the circle 0≤x<L, can be written in Hamiltonian formQ ^⊙ =?H/?P, P ^⊙ =??H/?Q with $$P = Q^\cdot and H = \tfrac{1}{2}\mathop \smallint \limits_0^L (Q')^2 + \mathop \smallint \limits_0^L F(Q) + \tfrac{1}{2}\mathop \smallint \limits_0^L P^2 ;$$ the corresponding flow preserves the (suitably interpreted) “petit ensemble”e ^?H d ^∞ Qd ^∞ P; and forL↓∞,Q settles down to the stationary diffusion with infinitesimal operator 1/2 ?²/?Q ²+m(Q)?/?Q,m being the logarithmic derivative of the ground state of ?d ²/dQ ² ‖F(Q). This diffusion is the “Brownian motion with restoring drift”; see McKean-Vaninsky [1993(1)]. For reasons suggested by the paper of Lebowitz-Rose-Speer [1988] on NLS, it is interesting to study the “micro-canonical ensemble” obtained by restricting to the sphere $\int\limits_0^L {Q^2 } = N$ and makingL↓∞ with fixedD=N/L. Now, forF(Q)/Q ²→∞, the same type of diffusion appears, but with drift arising from the modified potentialF(Q)+cQ ²,c being chosen so that the mean ofQ ² is the assigned numberD. The proof employs Döblin's method of “loops” [1937] and steepest descent. The same is true forF(Q)=m ² Q ², only now the proof is elementary. The outcome is also the same ifF(Q)/Q ²→0, providedD is smaller than the petit canonical mean ofQ ²; forD larger than this mean, the matter is more subtle and the outcome is unknown.     

AES-depth-profiling of thin annealed Pt-films on Si(100)

Thin PtSi films can be grown by evaporating Pt on Si(100) at RT and subsequent annealing of the system at 600–700 K. Contaminants like oxygen are known to have a strong influence on this reaction. In the present study we concentrate on the effect of oxygen partial pressure during the annealing on the silicide growth process. Under proper vacuum conditions annealing at 500 K leads to a homogeneous Pt₂Si film which reacts around 600 K completely to PtSi. A substantial oxygen partial pressure ( 0.1 mbar) in contrast results in an incomplete reaction in the same temperature range: unreacted platinum remains at the surface separated from the silicide by an oxygen enriched layer.Presented at the Seminar on Secondary Electrons in Electron Spectroscopy, Microscopy, and Microanalysis, Chlum (The Czech Republic), 21–24 September, 1993.This work was supported by Deutsche Forschungsgemeinschaft (DFG) through Sonderforschungsbereich 292.We thank Dr. W. Platz (Deutsche Aerospace AG, Ottobrunn) for providing us with Pt evaporated Si-wafers and Th. Hierl (Lehrstuhl für Angewandte Physik, University of Erlangen-Nürnberg), who performed the RBS measurements for AES calibration.     

Excitonic detectors of infrared and submillimeter radiation

The theory of new type detectors based on the quenching of secondary emission in direct-gap semiconductors (lines of Raman light scattering due to interaction between free and bound excitons in the crystal, and also bands of edge radiation) caused by IR or submillimeter radiation is proposed. The results obtained are confirmed by the experiment performed for CdS crystal excited by ultraviolet radiation of mercury lamp, at liquid helium temperature.     

Relaxed excited states and anomalous hyperfine structure of muonium centers in KBr

We report on the luminescence induced by positive muons implanted (with 4 MeV) into KBr crystal, which evidences a long-lived (lifetime=13.3 s excited state produced by muon radiolysis. The temperature dependence of the luminescence yield has a strong correlation with the amplitude of an anomalous muonium center: both are observed only below 50 K. This correlation strongly suggests that the muonium center is perturbed by the muon-induced excitons to cause the anomalous hyperfine structure. Moreover, the luminescence energy and decay time indicate that the observed luminescence is not associated with the intrinsic or impurity-related self-trapped excitons, but with a relaxed excited state specific to the muon(ium)-KBr system.