Nonlinear Effects for Bose Einstein Condensates in Optical Lattices

Cold atoms and, more recently, Bose-Einstein condensates （BEC＇s） in optical lattices have attracted increasing interest since their first realization. In particular, the formal similarity between the wavefunction of a BEC inside the periodic potential of an optical lattice and of the electrons in a crystal lattice has triggered theoretical and experimental efforts alike. Many phenomena from condensed matter physics, such as Bloch oscillations and Landau-Zener tunneling have been shown to be observable also in optical lattices. An important difference between electrons in a crystal lattice and a BEC inside the periodic potential of an optical lattice is the strength of the self interaction and hence the magnitude of the nonlinearity of the system. Electrons in a metal are almost noninteracting, whereas atoms inside a BEC interact strongly. A＇ perturbation approach is appropriate in the former case while in the latter the full nonlinearity must be taken into account. From this feature new physics is expected. Most experiments to date have been carried out in the regime of shallow lattice depth, for which the system is well described by the mean field Gross-Pitaevskii equation with a periodic potential. Moreover, the nonlinearity induced by the mean-field of the condensate has been shown, both theoretically and experimentally, to give rise to instabilities in certain regions of the Brillouin zone. These instabilities are not present in the corresponding linear system, i.e. the electron system. Experimental and theoretical results on the subject of nonlinear Landau-Zener tunneling and nonlinearity-induced instabilities in a Bose-Einstein condensate interacting with an external periodic potential will be presented.     

First chemical study of anaspidean Syphonota geographica: structure of degraded sterols aplykurodinone-1 and -2

Two unprecedented degraded sterols, aplykurodinone-1 (1) and -2 (2), have been isolated from the skin of the marine anaspidean Syphonota geographica, collected along the coasts of Greece. The structures and the relative stereochemistry were established by spectroscopic analysis and confirmed by chemical correlation with related known compounds.     

Catalysis in aprotic solvents. Effect of the polarity of the catalyst.

The catalytic constants for the $\text{n}$-butylaminolysis of sultones in aprotic-apolar solvents are linearly correlated with a combination of the hydrogen-bonding parameter and the polarity parameter of the catalyst.     

Water wafers: structure and melting of a hydrate inclusion compound of a neutral Pt(IV) complex with 1-methylcytosinato ligands

The characterization by X-ray analysis of the trans,trans,trans-[bis(1-methylcytosinate,N4)bis(ammine)bis(hydroxo)platinum(IV)] octahydrate complex (I) reveals an unexpected crystal packing. The neutral complex molecule is hosted by layers, totally built up by water molecules which do not exhibit a direct coordination to metal ions. These corrugated layers are made by puckered eight- and planar four-membered rings of water molecules, held together by hydrogen bonds with an ordered proton arrangement.     

Ab initio molecular modeling of 13C NMR chemical shifts of polymers. 1. Ethylene–norbornene copolymers

Cycloolefin copolymers (COC) have recently raised much interest because of their excellent thermal and optical properties, largely determined by the chain composition and stereochemistry. Previous force‐field computations allowed us to define the main conformational characteristics of ethylene–norbornene (E–N) copolymers and to contribute to the elucidation of their microstructure on the basis of empirical relationships between conformation and ¹³C nuclear magnetic resonance (NMR) chemical shifts. A thorough test of ab initio ¹³C chemical shifts computations [gauge‐invariant atomic orbitals (GIAO)] on known cases shows that the agreement with experimental data is quite good, especially with the MPW1PW91 density functional theory (DFT), using the 6‐311+G(2d,p) basis set on properly energy‐minimized structures. We applied this method on proper model compounds to confirm the signal assignment of the spectra of E–N copolymers in the presence of norbornene microblocks, where strong effects arising from ring distortions are expected to occur. The results nicely confirm the latest assignment of norbornene signals belonging to ENNE sequences. This shows the great potentialities of GIAO/DFT computations with regard to complex spectra interpretation and polymer microstructural investigations. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Synthesis and properties of some tetracyclic derivatives of 9H-carbazole, 10,11-dihydro-5H-dibenz[b,f]azepine,and 5,11-dihydrodibenz[b,e] [1,4]oxazepine

The behavior of 5,6-dihydro-4H-pyrido[3,2,1-jk]carbazol-4-one (10) , 1,2,7,8-tetrahydro-3H-quino[1,8-ab][1]benzazepin-3-one (11) , 1,2-dihydro-9H-[1]benzazepino[1,9-ab] [4,1]benzoxazepin-4 (3H)one (13) , and 1,2-dihydro-8H-[1]benzazepino[1,9-cd] [1,5]benzoxazepin-4(3H)one (14) towards the Schmidt reaction has been determined in polyphosphoric acid and in benzeneor chloroform-sulfuric acid. Evidence for the structure of the new heterocyclic systems obtained from these four compounds is presented.