Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

Confinement in a planar waveguide with porous silicon omnidirectional mirrors as confining walls

We present the design and study of waveguide structures based on porous silicon where the light confinement is not due to the usual total reflection effect but to the use of photonic crystals (PCs) as confining walls. These PC are omnidirectional mirrors (OMs), consisting of the periodic repetition of two porous silicon layers with different refractive indices and thicknesses. They reflect the radiation for all angles of incidence within a frequency range called the omnidirectional band gap (OBG). We have followed the PC formalism to investigate the properties of the OM as a multimode waveguide: the number of modes within the band gap, their field spatial distribution and their confinement as a function of the frequency and the core thickness.     

Spatial coherence and coherent interactions of broadband dispersed laser beams

Analytical expressions are obtained that describe the changes in the degree of coherence and in the thickness of the coherence layers occurring upon propagation of a dispersed broadband laser beam. It is found that the greater the tilting of the coherence layers with respect to the phase fronts, the more rapidly the spatial coherence is violated with increasing distance. A comparison with the case of an undispersed beam is performed. It is shown that, as the beam propagates, the decrease in the degree of coherence is accompanied by the appearance of spatial fluctuations of this parameter. The degree of mutual coherence of intersecting dispersed beams with parallel correlated coherence layers, which determines the efficiency of their coherent interaction, is investigated. The existence of spatial fluctuations of the degree of mutual coherence is established.     

Studying the process of ionization of hydrogen in conditions of its forced delivery to a porous nickel oxide electrode

The hydrogen ionization process is studied experimentally on an industrial sintered nickel oxide electrode in models of sealed nickel-metal hydride batteries. It is shown that the hydrogen ionization rates that are reached during overcharge by high current densities in conditions of forced gas delivery into the electrode pores (up to 40 mA cm^?2) exceed the self-discharge rate of a nickel-hydrogen battery by two orders of magnitude. Up to 70% of hydrogen delivered into the compact assembly block undergoes ionization during forced charge of models of sealed nickel-metal hydride batteries with a closed hydrogen cycle. Two independent methods (potentiostatic and manometric) are used to determine the relationship between rates of hydrogen ionization with the degree of the electrode filling with gas and perform estimation of the process intensity at a unit reaction surface. It is established that, in conditions of forced gas delivery, practically all the hydrogen oxidation current is generated at the surface of the nickel oxide electrode beneath thin films of an electrolyte solution at the rate of 4–5 mA cm^?2. It is shown that the hydrogen oxidation rate on a nickel oxide electrode filled in part by gas is independent of the electrode potential, probably because of a tangible contribution made by diffusion limitations to the overall hampering of the process.     

Effects of sputter deposition parameters and post-deposition annealing on the electrical characteristics of LaAlO3 dielectric films on Si

The influence of processing parameters on the electrical characteristics of RuO₂/LaAlO₃/Si metal-oxide-semiconductor structures was investigated. In particular, the sputtering regime during deposition of LaAlO₃ on Si and the atmosphere used in the post-deposition annealing step were addressed by determining capacitance-voltage and gate current-voltage characteristics. These results were correlated with compositional information obtained by Rutherford backscattering spectrometry and nuclear reaction analysis. A post-deposition annealing step in oxygen at 600 °C resulted in better electrical characteristics of the final structure as compared to the same treatment performed in nitrogen. This result is explained by oxygen ability to heal oxygen vacancies in the LaAlO₃ film, especially at the dielectric/semiconductor interface region. A thermalized sputtering regime during deposition of LaAlO₃ on Si leads to capacitors with electrical characteristics superior to those deposited in ballistic regime. PACS 77.84.Dy; 81.15.Cd; 81.40.Gh; 73.40.Qv; 82.80.Yc     

Some Estimates for the Derivative of a Quasiconformal Reflection Spiral-Shaped Domains

Some estimates of derivatives are sharpened for quasiconformal reflections of a special class of simply connected plane domains. Bibliography: 2 titles.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001