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

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

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

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

Synthesis, characterization, and thermal and surface properties of co- and terpolymers based on fluorinated α-methylstyrenes and styrene

Conventional bulk radical co- and terpolymerizations of α-fluoromethylstyrene (FMST) or/and α-trifluoromethylstyrene (TFMST) with styrene (ST) initiated by α,α′-azobis(isobutyronitrile) (AIBN) are presented. The resulting poly(F-ST-co-ST) copolymers and poly(TFMST-ter-ST-ter-FMST) terpolymers were characterized by 1H, 19F and/or 13C NMR spectroscopy that evidenced the incorporation of fluorinated α-methylstyrenes and enabled the assessment of the molar percentages of base units (in copolymers, 10.2–49.7 mol% of FMST and 10.6–48.3 mol% of TFMST and in terpolymers, F-ST mol% ranging between 5.2–38.4 and 3.7– 14.5 for FMST and TFMST, respectively). The molecular weights were in the range of 1500–23 700 g mol−1, 1500–14 600 g mol−1 and 6900–10 900 g mol−1 for poly(FMST-co-ST) and poly(TFMST-co-ST) copolymers and poly(TFMST-ter-ST-ter-FMST) terpolymers, respectively. The bulkier CF3 group induced a slightly lower reactivity of the TFMST comonomer. From the extended Kelen–Tüdős (EK–T) linear method, the kinetics of the copolymerizations led to the determination of the reactivity ratios, ri, of both comonomers for each copolymerization system (rFMST = 0.08 ± 0.02 and rST = 0.72 ± 0.04, rTFMST = 0.00 and rST = 0.64 ± 0.01 at 70 °C), showing that F-ST monomers were less reactive than ST and retarded the rate of polymerization, and thus reduced the molecular weights. However, in the case of terpolymerizations where all three monomers were incorporated into polymeric chains, the retarding effects of F-STs were less noticeable, indicating that a termonomer induced copolymerization occurred. Finally, the thermal properties of these copolymers showed that the presence of fluorinated monomer units incorporated into the polystyrenic structure promoted an increase of the glass transition temperatures of the resulting copolymers up to 114 °C [poly(TFMST-co-ST) copolymer] and a slightly better thermal stability than that of polystyrene. Furthermore, the relationships between the surface structure of varied fluorinated copolymers and their wetting and oleophobic properties showed that below 80 mol% of styrene repeating units, the incorporation of 20–40 mol% of FMST or 10–20 mol% of TFMST in the copolymer structure caused a major change in the contact angle of the copolymers, reaching an unexpectedly high water contact angle of up to 147°

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