Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

A Bicriterial Optimization Problem of Antenna Design

In this paper we consider a special optimization problem withtwo objectives which arises in antenna theory. It is shown that thisabstract bicriterial optimization problem has at least one solution.Discretized versions of this problem are also discussed, and therelationships between these finite dimensional problems and the infinitedimensional problem are investigated. Moreover, we presentnumerical results for special parameters using a multiobjectiveoptimization method.     

运动水平平板上混合对流的群论分析

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72　和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。     

Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators

This paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.     

The Potts model representation and a Robinson–Schensted correspondence for the partition algebra

We construct a correspondence between the set of partitions of a finite set M and the set of pairs of walks to the same vertex on a graph giving the Bratteli diagram of the partition algebra on M. This is the precise analogue of the correspondence between the set of permutations of a finite set and the set of pairs of Young tableaux of the same shape, called the Robinson–Schensted correspondence.     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Effective-Field Theory on High Spin Systems with Biaxial Crystal Field

Based on the effective-field theory with self-spin correlations and the differential operator technique,physical properties of the spin-2 system with biaxial crystal field on the simple cubic, body-centered cubic, as well as faced-centered lattice have been studied. The influences of the external longitudinal magnetic field on the magnetization,internal energy, specific heat, and susceptibility have been discussed in detail. The phenomenon that the magnetization in the ground state shows quantum effects produced by the biaxial transverse crystal field has been found.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

Chemical reactivity of hypervalent silicon compounds: The local hard and soft acids and bases principle viewpoint

The silicon atom may increase its coordination number to values greater than four, to form pentacoordinated compounds. It has been observed experimentally that, in general, pentacoordinated compounds show greater reactivity than tetracoordinated compounds. In this work, density functional theory is used to calculate the global softness and the condensed softness of the silicon atom for SiH _n F_4−n and SiH _n F _5−n ¹⁻ . The values obtained show that the global and condensed softness are greater in the pentacoordinated compounds than in the tetracoordinated compounds, a result that explains the enhanced reactivity. If the results are analysed through a local version of the hard and soft acids and bases principle, it is possible to suggest that in nucleophilic substitution reactions, soft nucleophiles preferably react with SiH _n F _5−n ¹⁻ , and hard nucleophiles with SiH _n F_4−n .