title: Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer.
abstract: We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type. Large noise is also seen to renormalize the bare physical parameters of the ring, akin to analogous parameter renormalization for equilibrium three-dimensional membranes. Our results bear particular importance on the relation between relevant universality classes of scale-invariant systems in two dimensions.
authors.affiliation: Departamento de Física and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Leganés, Spain.
authors.forename: Silvia N
authors.initials: SN
authors.lastname: Santalla
authors.affiliation: ICFO-Institut de Ciències Fotòniques, Castelldefels, Spain and Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain.
authors.forename: Javier
authors.initials: J
authors.lastname: Rodríguez-Laguna
authors.affiliation: Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain.
authors.forename: Rodolfo
authors.initials: R
authors.lastname: Cuerno