Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.     

Communication: An Improved Synthesis of Methyl 2,3-Anhydro-α and β-D-Lyxofuranosides

Methyl 2,3-anhydro-α (6) and β (7)-D-lyxofuranosides are important intermediates in the synthesis of C-3 substituted derivatives of D-arabinose which show biological activity as a tumor inhibitor.^1,2 Some syntheses of 6 and 7 are reported but they are either expensive or give poor yields ^3-4 and generally the authors refer to Baker and coll.⁵ who synthesized both α and β epoxides from D-xylose in five steps; yields were 28% and 22% respectively. This synthesis is very well described but reaction times and workups are long and several intermediates are distilled with difficulty under reduced pressure. Unger and coll.⁶, using Baker's method, improved the yield of compound 6 and Martin and coll.⁷ described a three steps synthesis of 6 but the final purification is very difficult and the use of mercuric reagents is not consistent with biological activity; furthermore these two publications concern only α anomer 6.     

The far-infrared absorption of a periodic 2DEG in the transition regime between weak and strong modulation

We study the optical absorption of arrays of quantum dots and antidots in a perpendicular homogeneous magnetic field. The electronic system is described quantum mechanically using a Hartree approximation for the mutual Coulomb interaction of the electrons. The evolution of the absorption is traced from the homogeneous to the strongly modulated case identifying the ensuing collective modes, the magnetoplasmons, and their correlations with inherent length scales of the system.     

The influence of the flexoelectric effect on the electrohydrodynamic instability in nematics

A rigorous three-dimensional linear analysis of the electrohydrodynamic instability in nematic liquid crystals including the flexoelectric effect is presented for the case of an applied d.c. voltage. The flexoelectric effect leads to an appreciable reduction of the threshold and to the appearance of oblique rolls at threshold for the standard material MBBA. We discuss the influence of a magnetic field and test several approximations against the rigorous results