Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.Comment: 16 pages, 7 figure

Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B), Gaussian copolymers, in dilute solutions. Using the multiple scattering technique, we have computed the diffusion and the friction coefficients D_AB and Zeta_AB, and the change Eta_AB in the viscosity of the solution as functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments of the A block and of the whole copolymer, respectively, and l_A, l_B are the Kuhn lengths of the A and B blocks. Specific regimes that maximize the efficiency of separation of copolymers with distinct "t" values, have been identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty, submitted to Macromolecule

On Supermultiplet Twisting and Spin-Statistics

Twisting of off-shell supermultiplets in models with 1+1-dimensional spacetime has been discovered in 1984, and was shown to be a generic feature of off-shell representations in worldline supersymmetry two decades later. It is shown herein that in all supersymmetric models with spacetime of four or more dimensions, this off-shell supermultiplet twisting, if non-trivial, necessarily maps regular (non-ghost) supermultiplets to ghost supermultiplets. This feature is shown to be ubiquitous in all fully off-shell supersymmetric models with (BV/BRST-treated) constraints.Comment: Extended version, including a new section on manifestly off-shell and supersymmetric BRST treatment of gauge symmetry; added reference

Nilpotent Classical Mechanics

The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates $\eta$. Necessary geometrical notions and elements of generalized differential $\eta$-calculus are introduced. The so called $s-$geometry, in a special case when it is orthogonally related to a traceless symmetric form, shows some resemblances to the symplectic geometry. As an example of an $\eta$-system the nilpotent oscillator is introduced and its supersymmetrization considered. It is shown that the $R$-symmetry known for the Graded Superfield Oscillator (GSO) is present also here for the supersymmetric $\eta$-system. The generalized Poisson bracket for $(\eta,p)$-variables satisfies modified Leibniz rule and has nontrivial Jacobiator.Comment: 23 pages, no figures. Corrected version. 2 references adde

On the Construction and the Structure of Off-Shell Supermultiplet Quotients

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do not produce Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.Comment: 20 pages, revised to clarify the problem addressed and solve

Plasticization and antiplasticization of polymer melts diluted by low molar mass species

An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization leads to a decreased glass transition temperature T_g and a "softening" of the fragile host polymer in the glass state. Plasticization is prompted by small additives with weakly attractive interactions with the polymer matrix. The shifts in T_g of polystyrene diluted by fully flexible short oligomers are evaluated from the computations, along with the relative changes in the isothermal compressibility at T_g to characterize the extent to which the additives act as antiplasticizers or plasticizers. The theory predicts that a decreased fragility can accompany both antiplasticization and plasticization of the glass by molecular additives. The general reduction in the T_g and fragility of polymers by these molecular additives is rationalized by analyzing the influence of the diluent's properties (cohesive energy, chain length, and stiffness) on glass formation in diluted polymer melts. The description of glass formation at fixed temperature that is induced upon change the fluid composition directly implies the Angell equation for the structural relaxation time as function of the polymer concentration, and the computed "zero mobility concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure

A representation formula for maps on supermanifolds

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation formula for all morphisms from the algebra of functions on an ordinary manifolds to the superalgebra of functions on an open subset of R^{p|q}. We then derive two consequences of this result. The first one is that we can integrate the data associated with a morphism in order to get a (non unique) map defined on an ordinary space (and uniqueness can achieved by restriction to a scheme). The second one is a simple and intuitive recipe to compute pull-back images of a function on a manifold by a map defined on a superspace.Comment: 23 page

Surface Polymer Network Model and Effective Membrane Curvature Elasticity

A microscopic model of a surface polymer network - membrane system is introduced, with contact polymer surface interactions that can be either repulsive or attractive and sliplinks of functionality four randomly distributed over the supporting membrane surface anchoring the polymers to it. For the supporting surface perturbed from a planar configuration and a small relative number of surface sliplinks, we investigate an expansion of the free energy in terms of the local curvatures of the surface and the surface density of sliplinks, obtained through the application of the Balian - Bloch - Duplantier multiple surface scattering method. As a result, the dependence of the curvature elastic modulus, the Gaussian modulus as well as of the spontaneous curvature of the "dressed" membrane, ~{\sl i.e.} polymer network plus membrane matrix, is obtained on the mean polymer bulk end to end separation and the surface density of sliplinks.Comment: 15 pages with one included compressed uuencoded figure