2D Lattice Liquid Models

A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on the rectangular honeycomb lattice of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability, and peculiar anomalous diffusions in their time-averaged mean square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.Comment: REVTeX4, 14 pages in double colomn, 12 figures; added references with some comments, typos fixe

Classical Hamiltonian Reduction On D(2∣1;α)D(2|1;\alpha) Chern-Simons Gauge Theory and Large N=4 Superconformal Symmetry

3d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;\alpha)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in $D(2|1;\alpha)$ CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties.Comment: LaTeX 13 pages, 1 figure; one reference added, some improvements mainly in section