Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

The WCl6-e-Al-CH2Cl2 catalyzed polypentenamer formation via ring-opening metathesis polymerization (ROMP)

The synthesis of polypentenamer by an electrochemically generated metathesis polymerization catalyst from methylene chloride solution of WCl₆ was investigated. The active species formed by electroreduction of this salt under controlled potential of +900 mV at a platinum cathode with an aluminum anode were found to catalyze the ring-opening metathesis polymerization (ROMP) of cyclopentene, monocyclic olefin of relatively low strain, in high yield (89%) and at short period (32 min) under mild conditions. The effect of reaction parameters, e.g., olefin/catalyst ratio, reaction time, electrolysis time, catalyst aging, on the polymerization yield have been studied. The resulting polymer has been characterized by ¹H and ¹³C NMR, IR and gel permeation chromatography (GPC) techniques. Analysis of the polypentenamer microstructure by means of ¹³C NMR spectroscopy indicates that the polymer contains a mainly trans stereoconfiguration of the double bonds (σ_c = 0.31) and a slightly blocky distribution (r_tr_c > 1) of cis and trans double bond dyads (r_tr_c = 1.44). However, this electrochemical system is reluctant to facilitate the competing vinyl type addition polymerization reactions.     

New analytical expressions,symmetry relations and numerical solutions for the rotational overlap integrals

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The taxicab space group

It is shown that the group of isometries of the 3-dimensional space with respect to taxicab metric is the semi-direct product of octahedral group O _h and T(3), where O _h is the (Euclidean) symmetry group of the regular octahedron and T(3) is the group of all translations of the 3-dimensional space.     

A Comparison of the LVDP and ΛCDM Cosmological Models

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the ΛCDM model. We show that the LVDP model is almost indistinguishable from the ΛCDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.     

Product factorability of integral bilinear operators on Banach function spaces

Positivity - This paper deals with bilinear operators acting in pairs of Banach function spaces that factor through the pointwise product. We find similar situations in different contexts of the...     

QC-DMRG study of the ionic-neutral curve crossing of LiF

We have studied the ionic-neutral curve crossing between the two lowest ¹Σ⁺ states of LiF in order to demonstrate the efficiency of the quantum chemistry version of the density-matrix renormalization group method (QC-DMRG). We show that QC-DMRG is capable of calculating the ground and several low-lying excited state energies within the error margin set up in advance of the calculation, while with standard quantum chemical methods it is difficult to obtain a good approximation to full configuration-interaction property values at the point of the avoided crossing. We have calculated the dipole moment as a function of bond length, which in fact provides a smooth and continuous curve even close to the avoided crossing, in contrast to other standard numerical treatments.     

Electron-phonon interaction and coulomb pseudopotential in AuGa alloys from resistivity and superconductivity measurements

Measurements of the electrical resistivity as a function of temperature from 250 to 270 K for Au and f.c.c. phase AuGa alloys are presented. The linear dependence of the resistivity with temperature and previous results of the superconducting transition temperature of the alloys are used to obtain a value for T_c of pure Au. From these results a new method is introduced to estimate the Coulomb pseudopotential μ¹ for gold.