The long delayed solution of the Bukhvostov Lipatov model

In this paper I complete the solution of the Bukhvostov Lipatov model by computing the physical excitations and their factorized S matrix. I also explain the paradoxes which led in recent years to the suspicion that the model may not be integrable.Comment: 9 page

On the Integrability of the Bukhvostov-Lipatov Model

The integrability of the Bukhvostov-Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary actions. It is then established that the conservation law is spoiled at the quantum level -- a fact that might indicate that the quantum Bukhvostov-Lipatov model is not integrable, contrary to what was previously believed.Comment: 11 pages, 1 figure, LaTeX2e, AMS; new references adde

Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine $sl(3)^{(1)}$ Toda model coupled to matter fields (CATM). The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The $sl(n)^{(1)}$ case is also outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions unchanged, to appear in J. Math. Phy

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.Comment: 25 pages, harvmac macros Report USC-95-001

Exact Friedel oscillations in the g=1/2 Luttinger liquid

A single impurity in the 1D Luttinger model creates a local modification of the charge density analogous to the Friedel oscillations. In this paper, we present an exact solution of the case $g={1\over 2}$ (the equivalent of the Toulouse point) at any temperature $T$ and impurity coupling, expressing the charge density in terms of a hypergeometric function. We find in particular that at $T=0$, the oscillatory part of the density goes as $\ln x$ at small distance and $x^{-1/2}$ at large distance.Comment: 1 reference added. 13 pages, harvma

Tunneling in quantum wires I: Exact solution of the spin isotropic case

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case ($g_\sigma=2$, $g_\rho$ arbitrary). The resulting integrable model is similar to a two channel anisotropic Kondo model, but with the impurity spin in a "cyclic representation" of the quantum algebra $su(2)_q$ associated with the anisotropy. Using exact, non-perturbative techniques we study the RG flow, and compute the DC conductance. As expected from the analysis of Kane and Fisher we find that the IR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.Comment: Revtex, epsf, 14pgs, 4 figs. One reference adde

Smart soils track the formation of pH gradients across the rhizosphere

Aims Our understanding of the rhizosphere is limited by the lack of techniques for in situ live microscopy. Current techniques are either destructive or unsuitable for observing chemical changes within the pore space. To address this limitation, we have developed artificial substrates, termed smart soils, that enable the acquisition and 3D reconstruction of chemical sensors attached to soil particles. Methods The transparency of smart soils was achieved using polymer particles with refractive index matching that of water. The surface of the particles was modified both to retain water and act as a local sensor to report on pore space pH via fluorescence emissions. Multispectral signals were acquired from the particles using a light sheet microscope, and machine learning algorithms predicted the changes and spatial distribution in pH at the surface of the smart soil particles. Results The technique was able to predict pH live and in situ within ± 0.5 units of the true pH value. pH distribution could be reconstructed across a volume of several cubic centimetres around plant roots at 10 μm resolution. Using smart soils of different composition, we revealed how root exudation and pore structure create variability in chemical properties. Conclusion Smart soils captured the pH gradients forming around a growing plant root. Future developments of the technology could include the fine tuning of soil physicochemical properties, the addition of chemical sensors and improved data processing. Hence, this technology could play a critical role in advancing our understanding of complex rhizosphere processes

Fluorinated Copolymers and Terpolymers Based on Vinylidene Fluoride and Bearing Sulfonic Acid Side-Group

International audienceThe radical co- and terpolymerization of perfluoro(4-methyl-3,6-dioxaoct- 7-ene) sulfonyl fluoride (PFSVE) with 1,1-difluoroethylene (or vinylidene fluoride, VDF or VF2), hexafluoropropene (HFP), chlorotrifluoroethylene (CTFE), and bromotrifluoroethylene (BrTFE) is presented. Although PFSVE could not homopolymerize under radical initiation, it could be copolymerized in solution under a radical initiator with VDF, while its copolymerizations with HFP or CTFE led to oligomers in low yields. The terpolymerizations of PFSVE with VDF and HFP, with VDF and CTFE, or with VDF and BrTFE also led to original fluorinated terpolymers bearing sulfonyl fluoride side-groups. The conditions of co- and terpolymerization were optimized in terms of the nature and the amount of the radical initiators, of the nature of solvents (fluorinated or nonhalogenated), and of the initial amounts of fluorinated comonomers. The different mol % contents of comonomers in the co- and terpolymers were assessed by 19F NMR spectroscopy. A wide range of co- and terpolymers containing mol % of PFSVE functional monomer ranging from 10 to 70% was produced. The kinetics of copolymerization of VDF with PFSVE enabled to assess the reactivity ratios of both comonomers: rVDF ¼ 0.57 6 0.15 and rPFSVE ¼ 0.07 6 0.04 at 120 8C. The thermal and physicochemical properties were also studied. Moreover, the glass transition temperatures (Tgs) of poly(VDF-co-PFSVE) copolymers containing different amounts of VDF and PFSVE were determined and the theoretical Tg of poly(PFSVE) homopolymer was deduced. Then, the hydrolysis of the SO2F into SO3H function was investigated and enabled the synthesis of fluorinated copolymers bearing sulfonic acid functions