Field theories with an infinite number of conservation laws and Bäcklund transformations in two dimensions

Field theories in two dimensions are generated from the integrability condition of a linear system which possesses Poincaré and internal symmetries. From matrix solutions of this system we get (i) an infinite set of non-local conserved currents and (ii) a family of one-parameter Bäcklund transformations. A large class of models is covered here, as the non-linear sigma, the SU(n) ? SU(n) and the non-abelian gauge invariant projector models.     

Ca1−xYxMnO3 manganites: synthesis and ESR characterization

Ceramic samples of Ca_1−xY_xMnO₃ were synthesized by a liquid-mix method obtaining single phase materials, for 0.1x1, with orthorhombic structure. The cell volume increases with x indicating that changes in the Mn electronic state overcomes the progressive diminishing of the (Ca, Y) cationic radius, r_Ca>r_Y. We observed a continuous broadening of the electronic spin resonance line width with x. This is explained in terms of the increasing orthorhombic distortions. We have measured the DC magnetization for the x=1 compound YMnO₃. Our results are compatible with a G-type antiferromagnet with T_N=44 K.     

Induced trees in sparse random graphs

The random graphG(n, p) onn vertices with edge probabilityp = c/n contains an induced tree of order _c n where _c > 0 forc > 1. This proves a conjecture of Erdös and Palka.     

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.     

Studies on quinones. VII. Synthesis of some benzo[b]thiophene-4,7-diones

The synthesis of methyl 4,7-dihydro-4,7-dioxobenzo[b]thiophene-2-carboxylate ( 20 ) based on the reaction of methyl mercaptoacetate with activated 1,4-benzoquinones is described. Methyl 4,7-dihydro-4,7-dioxo-5-hydroxybenzo[b]thiophene-2-carboxylate ( 24 ) and its corresponding methyl ether 26 were obtained through a Thiele-Winter acetoxylation on 20 . On the basis of the properties of methyl 4,7-dihydro-4,7-dioxo-6-methoxy-benzo[b]thiophene-2-carboxylate ( 21 ) obtained from 2,4,5-trimethoxybenzaldehyde ( 32 ), the structures of the products 24 and 26 are proposed.     

Application of HPTLC to the Analysis of Horminone in Sphacele chamaedryoides (Balbis) Briq.

JPC – Journal of Planar Chromatography – Modern TLC - Royleanones are diterpene quinones ubiquitous in plants belonging to the Lamiaceae family. Sphacele chamaedryoides is a plant used...     

Deterministic diffusion in almost integrable systems

Diffusion processes are usually associated with randomness in the system. In this paper we show that deterministic diffusion processes can also occur in systems with zero entropy that mimic chaos with any precision without being mathematically chaotic. A random walk model is used to predict the behavior of the diffusion coefficient. (c) 1996 American Institute of Physics.