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.     

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.     

Vibrational spectroscopic and conformational studies of 1-(4-pyridyl)piperazine

Possible stable conformers of the 1-(4-pyridyl)piperazine (1-4pypp) molecule were experimentally and theoretically studied by FT-IR and Raman spectroscopy. FT-IR and Raman spectra were recorded in the region of 4000–200 cm⁻¹. Optimized geometric structures related to the minimum on the potential energy surface were investigated by the B3LYP hybrid density functional theory method using the 6-31G(d) basis set. Comparison of the experimental and theoretical results indicates that the density functional B3LYP method provides satisfactory results for the prediction of vibrational wavenumbers and structural parameters and equatorial-equatorial (e-e) isomer is supposed to be the most stable form of the 1–4pypp molecule.     

Investigation of clinoptilolite rich natural zeolites from Turkey: a combined XRF,TG/DTG,DTA and DSC study

Turkey clinoptilolite-rich tuffs from Gördes and Bigadiç regions of western of Anatolia and their exchanged forms (K⁺, Na⁺, Mg²⁺ and Ca²⁺) were characterized by TG/DTG-DTA, DSC and XRF methods and the surface areas were also determined for both tuffs. TG-DTG and DTA curves of all clinoptilolite samples were measured in the temperature range 30–1000 °C. All clinoptilolite samples had major, rapid mass losses between 30 and 200 °C, with slower and less significant mass losses at higher temperatures. The mass loss of the Natural-G is 9.54% while that of the Natural-B sample is 10.50%. Water content increases in the order of K < Na < Ca < Mg for Bigadiç clinoptilolite samples and in the following sequence K < Na < Mg < Ca for Gördes clinoptilolite samples. One mass loss step for all clinoptilolite samples was observed using differential scanning calorimeter (DSC) in the range of 30–550 °C.     

Dye-sensitized solar cells fabricated with black raspberry, black carrot and rosella juice

In this work, dye sensitized solar cells (DSSC’s) were constructed from black raspberry (Rubus Ideaus), black carrot (Daucuscarota L.) and rosella juice (Hibiscus Sabdariffa L.). In order to fabricate a DSSC the fluorine-doped tin (IV) oxide (FTO) thin films obtained by using spray pyrolysis technique were used as a substrate. TiO₂ films on FTO layers were prepared by doctor-blading technique. Platinum-coated counter electrode and liquid Iodide/Iodine electrolyte solution were used to fabricate DSSC’s. The efficiencies of solar cells produced with black carrot, rosella and black raspberry juice were calculated as 0.25%, 0.16% and 0.16% respectively, under a sunny day in Kahramanmaraş-Turkey.     

Vibrational spectroscopic study on some Hofmann-Td type clathrates: Ni(4-phenylpyridine)2M(CN)4·2G (M=Cd or Hg, G=1,4-dioxane)

New Hofmann-T(d) type clathrates in the form of Ni(4-Phpy)(2)M(CN)(4)·2G (where 4-Phpy=4-phenylpyridine, M=Cd or Hg and G=1,4-dioxane) have been prepared in powder form and their FT-IR and Raman spectra have been reported. The results suggest that these compounds are similar in structure to the Hofmann-T(d) type clathrates.     

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.