Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts and Gels. I. General Formulation and Predictions

The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and compared to the corresponding reptation/ tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/N_e, where the entanglement degree of polymerization, N_e, can be measured from the plateau shear modulus. Two microscopically defined non-universal parameters, an entanglement strength 1/alpha and a length scale ratio, delta= xi_rho/b, where xi_rho and b are the density screening and entanglement length respectively, are shown to determine the reduction of the entanglement effects relative to the reptation- -like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees of polymerization up to N/N_e\le10^3. Effective power law variations for intermediate N/N_e of the viscosity, eta\sim N^x, and the diffusion constant, D\sim N^{-y}, can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x\ge 3 and y\ge2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Comment: Latex, figures and styles files included; Macromolecules, in press (1997

Recent developments in effective field theory

We will give a short introduction to the one-nucleon sector of chiral perturbation theory and will address the issue of a consistent power counting and renormalization. We will discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order O(q^6) and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors.Comment: 8 pages, 6 figures, invited talk given at International School of Nuclear Physics, 29th Course "Quarks in Hadrons and Nuclei", Erice, Sicily, 16 - 24 September 200

Analysis and interpretation of new low-energy Pi-Pi scattering data

The recently published E865 data on charged K_e4 decays and Pi-Pi phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters alpha and beta, of the low-energy constants l3-bar and l4-bar as well as of the main two-flavour order parameters: and F_pi in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on Pi-Pi phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2 a_0^0 - 5 a_0^2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-sigma level is found and commented upon.Comment: Published version, to appear in Eur. Phys. J.

Schnabl's L_0 Operator in the Continuous Basis

Following Schnabl's analytic solution to string field theory, we calculate the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the continuous $\kappa$ basis. We find an explicit and simple expression for them that further simplifies for their sum, which is block diagonal in this basis. We generalize this result for the bosonized ghost sector, verify their commutation relation and relate our expressions to wedge state representations.Comment: 1+16 pages. JHEP style. Typos correcte