Form-factors of exponential fields in the sine-Gordon model

An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.Comment: 8 pages, harvmac.tex, added the formula (25) for two soliton form-factors at the reflectionless point

Transport of interacting electrons through a potential barrier: nonperturbative RG approach

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) \beta-function are identified. A universal part of the \beta-function is given by a ladder series and summed to all orders in g_2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature dependent conductance is solved analytically. Our result agrees with known limiting cases.Comment: 6 pages, 5 figure

Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory

We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized dyrectly in the SG field theory, we are rather concerned here with the corresponding N-soliton solutions. We present explicit expressions for their infinithesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.Comment: 17 pages, corrected some typos, two references adde

An Equation of State of a Carbon-Fibre Epoxy Composite under Shock Loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [Int. J. Plasticity \textbf{24}, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Gr\"{u}neisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity $U^{A}_{s}$ and particle velocity $u_{p}$ was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the $U^{A}_{s}$-$u_{p}$ relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship $U^{A}_{s}$-$u_{p}$ over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of $c^{A}_{0}$ (the intercept of the $U^{A}_{s}$-$u_{p}$ curve) that is in the range between first and second generalised anisotropic bulk speed of sound [Eur. Phys. J. B \textbf{64}, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HELs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.Comment: 12 pages, 9 figure

`Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the ''composite particles'' in terms of creation operators attached to the Young tableaux. Using the technique of bosonisation, we obtain a position space representation of the ''composite particles'' in terms of products of vertex operators. In the special case where the ''composite particles'' are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series $\nu =p/(2np\pm 1)$ of the fractional quantum Hall effect.Comment: latex calcomp2.tex, 5 files, 30 pages [SPhT-T99/080], submitted to J. Math. Phy

Particle-Field Duality and Form Factors from Vertex Operators

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values of such vertex operators in the space of fields. The vertex operators can be constructed explicitly in radial quantization. Furthermore, these vertex operators can be exactly bosonized in momentum space. We develop these ideas by studying the free-fermion point of the sine-Gordon theory, and use this scheme to compute some form-factors of some non-free fields in the sine-Gordon theory. This work further clarifies earlier work of one of the authors, and extends it to include the periodic sector.Comment: 17 pages, 2 figures, CLNS 93/??

Charge and matter distributions and form factors of light, medium and heavy neutron-rich nuclei

Results of charge form factors calculations for several unstable neutron-rich isotopes of light, medium and heavy nuclei (He, Li, Ni, Kr, Sn) are presented and compared to those of stable isotopes in the same isotopic chain. For the lighter isotopes (He and Li) the proton and neutron densities are obtained within a microscopic large-scale shell-model, while for heavier ones Ni, Kr and Sn the densities are calculated in deformed self-consistent mean-field Skyrme HF+BCS method. We also compare proton densities to matter densities together with their rms radii and diffuseness parameter values. Whenever possible comparison of form factors, densities and rms radii with available experimental data is also performed. Calculations of form factors are carried out both in plane wave Born approximation (PWBA) and in distorted wave Born approximation (DWBA). These form factors are suggested as predictions for the future experiments on the electron-radioactive beam colliders where the effect of the neutron halo or skin on the proton distributions in exotic nuclei is planned to be studied and thereby the various theoretical models of exotic nuclei will be tested.Comment: 26 pages, 11 figures, 3 tables, accepted for publication in Phys. Rev.