Anyon systems are studied in connection with several interesting applications including high $T_C$ superconductivity and topological quantum computing. In this work we show that these systems can be realized starting from directed polymers braided to
gether to form a nontrivial link configuration belonging to the topological class of plats. The statistical sum of a such plat is related here to the partition function of a two-component anyon gas. The constraints that preserve the topological configuration of the plat are imposed on the polymer trajectories using the so-called Gauss linking number, a topological invariant that has already been well studied in polymer physics. Due to these constraints, short-range forces act on the monomers or, equivalently, on the anyon quasiparticles in a way that closely resembles the appearance of reaction forces in the constrained systems of classical mechanics. If the polymers are homogeneous, the anyon system reaches a self-dual point, in which these forces vanish exactly. A class of self-dual solutions that minimize the energy of the anyons is derived. The two anyon gas discussed here obeys an abelian statistics, while for quantum computing it is known that nonabelian anyons are necessary. However, this is a limitation due to the use of the Gauss linking invariant to impose the topological constraints, which is a poor topological invariant and is thus unable to capture the nonabelian characteristics of the braided polymer chains. A more refined treatment of the topological constraints would require more sophisticated topological invariants, but so far their application to the statistical mechanics of linked polymers is an open problem.
The influence of the surface structure and vibration mode on the resistivity of Cu films and the corresponding size effect are investigated. The temperature dependent conductivities of the films with different surface morphologies are calculated by t
he algorithm based upon the tight-binding linear muffin-tin orbital method and the Greens function technique. The thermal effect is introduced by setting the atomic displacements according to the Gaussian distribution with the mean-square amplitude estimated by the Debye model. The result shows that the surface atomic vibration contributes significantly to the resistivity of the systems. Comparing the conductivities for three different vibration modes, it is suggested that freezing the surface vibration is necessary for practical applications to reduce the resistivity induced by the surface electron-phonon scattering.
