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.     

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.     

Copper(I)alkyl bonding in the dinuclear copper(I) compound [(CH3)2P(CH2)2]2Cu2

The complex of empirical formula Cu^I[(CH₃)₂(CH₂)₂P] has been found to be dimeric with two digonal copper(I) atoms bridged by two ligand molecules through coppercarbon σ-bonds, resulting in a centrosymmetric eight-membered heterocycle.     

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.     

Structural analyses and magnetic properties of 3D coordination polymeric networks of nickel(II) maleate and manganese(II) adipate with the flexible 1,2-bis(4-pyridyl)ethane ligand

Two novel inorganic-organic hybrid 3D extended networks of Ni(II) and Mn(II) having molecular formulas [(maleate)(2)Ni(3)(bpe)(4)(H(2)O)(4)](NO(3))(2).H(2)O (1) and [(adipate)Mn(bpe)] (2) (bpe = 1, 2-bis(4-pyridyl)ethane), respectively, have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature (300-2 K) magnetic measurements. Compound 1 crystallizes in the monoclinic system, space group C2/c (No. 15), with chemical formula C(56)H(62)N(10)Ni(3)O(19), a = 30.955(4) A, b = 12.705(3) A, c = 17.058(5) A, beta = 117.26(2) degrees, and Z = 4. Compound 2 crystallizes in the triclinic system, space group Ponemacr; (No. 2), with chemical formula C(18)H(20)MnN(2)O(4), a = 8.492(2) A, b = 9.444(2) A, c = 11.533(3) A, alpha = 97.19(1) degrees, beta = 94.64(1) degrees, gamma = 105.02(1) degrees, and Z = 2. The structure determination reveals for both a 3D network. Compound 1 contains two crystallographically independent Ni(II) ions in different octahedral environments. Ni(1) lies on an inversion center, and its coordination environment comprises two chelating maleate anions and two bpe nitrogen donors, while the Ni(2) ion is surrounded by meridionally disposed three bpe N atoms, two water molecules, and one oxygen donor from the dicarboxylate anion. Of the three crystallographic independent bpe ligand, one presents an anti and the others a gauche conformation. The corresponding N-to-N distances are 9.344, 6.543, and 6.187 A. Variable-temperature magnetic susceptibility measurement of the complex reveals the existence of a dominant ferromagnetic interaction within the molecule. Compound 2 is composed of Mn(2) dimer units linked by adipate anions to form corrugated 2D sheets which, on interconnection through bpe (anti conformation, N-to-N distance of 9.391 A), produces an interpenetrated 3D alpha-polonium-related type net. Complex 2 reveals to be antiferromagnetic fitting data using a dimeric Mn(II) model that considers negligible magnetic transmission through the carbon skeleton of adipate and the bpe pathway.     

Alcune caratterizzazioni della γ-convergenza multipla

Summary The main features considered in this paper are characterisations of multiple -convergence in the saddle function case and in the general case. The main results for saddle case are theorems II.1.1 II.1.2 II.2.1 III.3.3 III.3.4and for general case theorem IV.1.2. In the fifth section we introduce vF-convergence and give equivalence results between vF.

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