On a theoretical model for d-wave to mixed s- and d-wave transition in cuprate superconductors

A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. The transition occurs between a phase in which the system is a condensate of one of the bosons, and a phase which is a mixture of two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases and the temperature dependence of the heat capacity.Comment: 8 pages, 4 figure

Multifractals Competing with Solitons on Fibonacci Optical Lattice

We study the stationary states for the nonlinear Schr\"odinger equation on the Fibonacci lattice which is expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are called critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions, a forbidden region, the spectrum of critical states, and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact irrespective of the nonlinearity in the sea of a large number of stationary solitons.Comment: 5 pages, 4 figures, major revision, references adde

The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles

The Nonlinear Schroedinger Equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a random (Anderson like) potential has been done at various levels of control: numerical, analytical and rigorous. Yet, this model equation presents us with a highly inconclusive and often contradictory picture. We will describe the main recent results obtained in this field and propose a list of specific problems to focus on, that we hope will enable to resolve these outstanding questions.Comment: 21 pages, 4 figure

Synthesis and structure of novel substituted N-sulfinylanilines

© 2017, Pleiades Publishing, Ltd. N-Sulfinylanilines derived from 4-bromoaniline, 3-nitroaniline, and 4,4′-di(ethane-1,2-diyl)dianiline were synthesized. X-ray diffraction analysis of 4-bromo-N-sulfinylaniline, 3-nitro-N-sulfinylaniline, and 4,4′-(ethane-1,2-diyl)di-N-sulfinylaniline was performed. The sulfinyl function in the planar conformation of the Ar-NSO fragment was found to have Z configuration. The nature of intra- and intermolecular structure-forming interactions was established

Crystallization of racemic 4-arylsulfonyl-2(5H)-furanones: Reproducibility of homochiral associates, conditions for the spontaneous resolution of enantiomers and the formation of racemic compounds, the role of intermolecular interactions

Crystallization of three 4-arylsulfonyl-2(5H)-furanones from chloroform leads to the formation of a conglomerate of sulfone with para-tolyl substituent and racemic crystals of chloro and bromo analogs. The high degree of similarity of the crystal packings of a homochiral crystal and racemic compounds, viz., the similar type of the homochiral hydrogen-bonded chains and analogous three-dimensional homochiral layers additionally stabilized by the interactions of the type C=O.C=O and C-H.O, allowed us to suggest the presence of the second, "missing" form for each sulfone. A directed search for the "missing" forms revealed the existence of the racemic modification of sulfone with the para-tolyl fragment formed during a very slow crystallization of the compound from benzene. No conglomerates of bromo and chloro analogs were found. Topological analysis of the electron density distribution performed by quantum chemical calculations using density functional theory (PBE1PBE, 6-31G(d,p)) showed the higher energy favorability of intermolecular interactions in the homochiral chains as compared to the hypothetical heterochiral associates. © 2013 Springer Science+Business Media New York

Quantum diffusion with disorder, noise and interaction

Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a paradigmatic problem, the diffusion of a wavepacket, by employing ultra-cold atoms in a disordered lattice with controlled noise and tunable interaction. The presence of disorder leads to Anderson localization, while both interaction and noise tend to suppress localization and restore transport, although with completely different mechanisms. When only noise or interaction are present we observe a diffusion dynamics that can be explained by existing microscopic models. When noise and interaction are combined, we observe instead a complex anomalous diffusion. By combining experimental measurements with numerical simulations, we show that such anomalous behavior can be modeled with a generalized diffusion equation, in which the noise- and interaction-induced diffusions enter in an additive manner. Our study reveals also a more complex interplay between the two diffusion mechanisms in regimes of strong interaction or narrowband noise.Comment: 11 pages, 10 figure

Perturbation theory for the Nonlinear Schroedinger Equation with a random potential

A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small denominators was developed. It was shown that the number of terms grows exponentially with the order. The results of the perturbation theory are compared with numerical calculations. An estimate on the remainder is obtained and it is demonstrated that the series is asymptotic.Comment: 30 pages, 7 figures, accepted to Nonlinearit

Synthesis and properties of phosphabetaine structures: III. Phosphabetaines derived from tertiary phosphines and α,β-unsaturated carboxylic acids. Synthesis, structure, and chemical properties

Methods of synthesis of acylate phosphabetaines by reactions of triphenylphosphine with methacrylic, cinnamic, and p-methoxycinnamic acids are developed. The phosphabetaine form is proposed to exist in equilibrium with the (σ5-oxaphospholane form. The features of methylation of the phosphabetaines are discussed

Synthesis and properties of phosphabetaine structures: IV. 3-(triphenylphosphonio)propanoate in reactions with dipolar electrophilic reagents

Reactions of 3-(triphenylphosphonio)propanoate with heterocumulenes, such as phenyl isocyanate and dicyclohexylcarbodiimide, we studied under the assumption that they proceed by nucleophilic addition and 1,4-dipolar cycloaddition schemes. Quantum-chemical calculations show that the σ5-phosphorane cycloadduct of the betaine with isocyanate is thermodynamically preferred over its isomeric zwitter-ionic adduct. However, the experimental evidence suggests that the reaction with phenyl isocyanate involves nucleophilic addition of the betaine to isocyanate followed by hydrolysis to firm finally a complex of the starting betaine with diphenylurea. The structure of the complex was established by X-ray diffraction analysis. The revealed above controversy is explained by a high protophilicity of betaine structures, which is also confirmed by the results of the reaction of the betaine with carbodiimide. © Pleiades Publishing, Inc., 2006