Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters (lambda(x),lambda(y),lambda(z)). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ``BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., lambda(x) = lambda(y) = lambda(z)) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid He-3. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

Synthetic approaches to homogynolides A and B

A four step, efficient and general methodology for the conversion of a cyclic ketone into the corresponding alpha-spiro-beta-methylene-gamma-butyrolactone, the key structural feature present in tricyclic sesquiterpenes bakkanes, has been developed employing a regiospecific 5-exo dig radical cyclisation reaction as the key step. The methodology has been extended to the total synthesis of bakkanes including homogynolide-B and chiral homogynolide-A.

Synthetic Studies Towards Prismanes - Rearrangements In Some Pentacyclic Precursors And X-Ray Crystal-Structure Of A Novel Heptacyclic Ether

In order to gain access to the heptacyclic tetraone 3, efforts were directed towards the utilisation of the major 'unwanted' [4 + 2]-adduct 11 of tetrachlorodimethoxycyclopentadiene and norbornenobenzoquinone. Epoxides derived from the diol and dimethoxy derivatives of the adduct 11 undergo facile Wagner-Meerwein rearrangement resulting in the required endo, syn, endo stereochemistry as well as methano-bridge functionalisation to deliver 18 and 24, respectively. However, intramolecular ether formation, occurring via the capture of carbocation intermediate with the transannularly poised oxygen functionality, is a more facile process. Attempts to cleave the ether linkage resulted in the formation of a novel transannularly cyclised twisted bowl shape heptacyclic compound 30 and its structure has been established through X-ray crystallography.

Synthetic, spectroscopic and structural studies on uranium and thorium complexes of diphosphazane dioxides

Co-ordination complexes of the diphosphazane dioxides Ph(2)P(O)N(Pr-i)P(O)Ph(2) L(1). Ph(2)P(O)N(Pr-i)P(O)Ph(OC(6)H(4)Me-4) L(2) and Ph(2)P(O)N(Pr-i)P(O)(O2C12H8) L(3) with UO22+ or Th4+ ions have been synthesised and characterised by IR and NMR spectroscopy. The structures of [UO2(NO3)(2)L(1)] and [Th(NO3)(2)L(3)(1)][Th(NO3)(6)] are established by X-ray crystallography. In the former, the uranyl ion is bonded to two bidentate nitrate groups and the two phosphoryl groups of the ligand L(1); the co-ordination polyhedron around the metal is a hexagonal bipyramid. The cationic moiety in the thorium complex contains three bidentate diphosphazane dioxide ligands and two bidentate nitrate groups around the ten-co-ordinated metal.

Synthetic aperture radar: A focus on current problems

Synthetic aperture radar (SAR) is a powerful tool for mapping and remote sensing. The theory and operation of SAR have seen a period of intense activity in recent years. This paper attempts to review some of the more advanced topics studied in connection with modern SAR systems based on digital processing. Following a brief review of the principles involved in the operation of SAR, attention is focussed on special topics such as advanced SAR modelling and focussing techniques, in particular clutterlock and autofocus, Doppler centroid (DC) estimation methods involving seismic migration technique, moving target imaging, bistatic radar imaging, effects of system nonlinearities, etc.

Novel materials, materials design and synthetic strategies: recent advances and new directions

There have been major advances in solid state and materials chemistry in the last two decades and the subject is growing rapidly. In this account, a few of the important aspects of materials chemistry of interest to the author are presented. Accordingly, transition metal oxides, which constitute the most fascinating class of inorganic materials, receive greater attention, Metal-insulator transitions in oxides, high temperature superconductivity in cuprates and colossal magnetoresistance in manganates are discussed at some length and the outstanding problems indicated, We then discuss certain other important classes of materials which include molecular materials, biomolecular materials and porous solids. Recent developments in synthetic strategies for inorganic materials are reviewed. Some results on metal nanoparticles and nanotubes are briefly presented. The overview, which is essentially intended to provide a flavour of the subject and show how it works, lists references to many crucial reviews in the recent literature.

Synthetic studies directed towards the potent cytotoxic natural product ottelione A: stereoselective construction of the complete framework

A stereoselective strategy for the rapid acquisition of the complete framework (dideoxyottelione A) of the promising cytotoxic agent ottelione A, with four contiguous stereogenic centres on a hydrindane skeleton and a sensitive 4-methylenecyclohex-2-enone functionality, from the readily available Diels-Alder adduct of 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadiene and norbornadiene, is delineated.

Synthetic studies towards novel terpenic natural products kelsoene and poduran: Construction of the complete 4-5-5-fused tricarbocyclic core

A common synthetic approach to the recently reported sesquiterpene kelsoene 1 and the tetraterpene poduran 5, bearing a novel tricyclo[6.2.0.0(2,6)]decane framework, from commercially available 1,5-COD and leading to the first construction of the carbocyclic core present in these natural products is delineated.

Crystal and molecular structure of synthetic cholesterol compounds vitamin D3-analogues (I) 24(S)-hydroxy coprastan-3-one & (II) 24(R)-hydroxy coprastan-3-one

The title compound I (24-(S)-Hydroxy Coprastan-3-one) crystallises in orthorhombic space group P2(1)2(1)2(1) with Z = 4. The unit cell dimensions are a = 6.701(2)Angstrom, b = 11.506(8)Angstrom, c = 32.183(4)Angstrom, V = 2481(2)Angstrom (3), D-cal = 1.077 Mg/m(3). The tide compound II (24-(R)-Hydroxy Coprastan-3-one) crystallises in orthorhombic space group P212121 with two molecules per assymetric unit and with Z = 8. The Unit cell dimensions are a = 10.954(2)Angstrom, b = 21.757(6)Angstrom, c = 21.130(7)Angstrom, V = 5035.0(2)Angstrom (3), D-cal = 1.062 Mg/m(3). In compound I and in both the molecules of compound II, the rings A, B & C are in chair conformation and the five membered ring D is in envelope conformation. The priority sequence attached to the chiral carbon C24 has "S" designation in compound I and "R" designation in compound II. The structures are stabilized by C-H . . .O and O-H---O hydrogen bonds.

Novel metal oxides prepared by ingenious synthetic routes

Several novel oxides have been prepared by the decomposition of carbonate precursors of calcite structure of the general formulas Mn1−xMxCO3 (M = Mg,Co,Cd), Ca1−xMx'CO3, and Ca1−x−yMxMy”CO3.

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-1/2 fermions in three dimensions at a finite density (rho similar to k(F)(3)) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector lambda equivalent to (lambda(x),lambda(y),lambda(z)), whose magnitude lambda determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k(F)vertical bar a(s)vertical bar less than or similar to 1), the ground state in the absence of the gauge field (lambda = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (lambda = 0). For large gauge couplings (lambda/k(F) >> 1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)-we call these bosons ``rashbons.'' In the absence of interactions (a(s) = 0(-)), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling lambda(T). For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of lambda near lambda(T). In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

Synthetic Triterpenoid Cyano Enone of Methyl Boswellate Activates Intrinsic, Extrinsic, and Endoplasmic Reticulum Stress Cell Death Pathways in Tumor Cell Lines

We explored the effect of a novel synthetic triterpenoid compound cyano enone of methyl boswellates (CEMB) on various prostate cancer and glioma cancer cell lines. CEMB displayed concentration-dependent cytotoxic activity with submicromolar lethal dose 50% (LD(50)) values in 10 of 10 tumor cell lines tested. CEMB-induced cytotoxicity is accompanied by activation of downstream effector caspases (caspases 3 and 7) and by upstream initiator caspases involved in both the extrinsic (caspase 8) and intrinsic (caspase 9) apoptotic pathways. By using short interfering RNAs (siRNA), we show evidence that knockdown of caspase 8, DR4, Apaf-1, and Bid impairs CEMB-induced cell death. Similar to other proapoptotic synthetic triterpenoid compounds, CEMB-induced apoptosis involved endoplasmic reticulum stress, as shown by partial rescue of tumor cells by siRNA-mediated knockdown of expression of genes involved in the unfolded protein response such as IRE1 alpha, PERK, and ATF6. Altogether, our results suggest that CEMB stimulates several apoptotic pathways in cancer cells, suggesting that this compound should be evaluated further as a potential agent for cancer therapy. Mol Cancer Ther; 10(9); 1635-43. (C)2011 AACR.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Towards sustainability: a new, solid-state synthetic route for supported metal nanocatalysts

Noble metal ions like Pt(IV) and Pd(II) were impregnated on gamma-alumina and aerosol 300 silica surfaces. Reduction of these ions using ammonia borane in the solid state resulted in the formation of the respective metal nanoparticles embedded in BNHx polymer which is dispersed on the oxide support. Removal of the BNH polymer was accomplished by washing the samples repeatedly with methanol. In this process the polymer undergoes solvolysis to release H-2 accompanied by the formation of ammonium methoxy borate salt, which has been removed by repeated methanol washings. As a result, metal nanoparticles well dispersed on gamma-alumina and aerosol 300 silica were obtained. These samples have been characterized by a combination of techniques, including electron microscopy, powder X-ray diffraction, NMR spectroscopy and surface area analyser.