International Journal of Modern Physics B

Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of "How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why?" We will review some of our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally challenging.

High-temperature superconductors are nowadays found in great variety and hold technological promise. It is still an unsolved mystery that the critical temperature T_c of the basic cuprates is so high. The answer might well be hidden in a conventional corner of theoretical physics, overlooked in the recent hunt for exotic explanations of new effects in these materials. A forgotten intra-atomic s–d two-electron exchange in the Cu atom is found to provide a strong (~ eV) electron pairing interaction. A Bardeen–Cooper–Schrieffer approach can explain the main experimental observations and predict the correct d_x²-y² symmetry of the gap.

The pressure dependence of sound velocity of longitudinal and shear waves were measured up to 0.5 GPa using a pulse echo overlap method on polycrystalline single-phase MgB₂ superconductor which was high pressure synthesized and with a T_c of 39 K. The pressure dependence of Debye temperature and specific heat were calculated based on sound velocity data. The results indicate that Debye temperature increases with the applied pressures while specific heat decreases. The Grüneisen constant was calculated as well. From the sound velocities, the pressure coefficient of the averaged phonon frequency was obtained, which is consistent with the value estimated by Vogt et al. This indicates that the importance of phonon hardening in the variation of T_c under pressure. Upon changing the Debye temperature, unit cell volume and transition temperature with the pressure, volume dependence of electron-phonon coupling constant are also calculated.

In this work, a gauge approach to quantum computing is considered. It is assumed that there exists a classical procedure for placing certain classical system in a state described by a holomorphic vector bundle with connection with logarithmic singularities. This bundle and its connection are constructed with the aid of unitary operators realizing the given algorithm using methods of the monodromic Riemann–Hilbert problem. Universality is understood in the sense that for any collection of unitary matrices there exists a connection with logarithmic singularities whose monodromy representation involves these matrices.

The effect of coupling between the electronic transverse motion and longitudinal motion is considered in the theoretical investigation of the resonant tunneling in a semiconductor multi-barriers heterostructure. A numerical calculation is carried out for rectangular and parabolic-well heterostructures consisting of ZnSe/Zn_1-xCd_xSe. The result indicates that the coupling effect results in not only a movement of the resonant peaks but also a reduction of the peak-to-valley ratio in the transmission spectrum. The effect of the electronic transverse motion on the higher-lying resonant states for the resonant tunneling is more remarkable for both the zero and non-zero bias voltages. The J-V characteristic formula of tunneling current density, which is different from Esaki's result, is given by using a two-dimensional approximation. The influence of temperature and mixed crystal effect on the J-V characteristic is also investigated.

In general, fuzzy modeling requires two stages: structure identification (generating the fuzzy rule base) and parameter learning (optimizing parameters in fuzzy rules). Here, we present an on-line algorithm for competitive learning and optimization of fuzzy models. Differing from existing methods, in this approach the structure identification and parameter optimization of the fuzzy model can be carried out automatically, using on-line acquisition of data. We demonstrate this approach by applying it to different types of nonlinear system modeling.

By including a pre-phase-factor, the Moyal representation for the spin-1/2 (or two-level) system is modified. Such a modification is necessary for describing completely the quantum evolution and calculating exactly the quantum phase. In our modified Moyal representation (MMR) the geometrical expression of the most general quantum phase, i.e., the Pancharatnam phase, is deduced in a much simpler way and without the restriction of cyclic evolution. Two simple examples of application of the MMR are given.

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger scales. We apply our results to a rectangle with incommensurate sides and show that they are in excellent agreement with the limiting cases established in the semiclassical theory of level rigidity.