title: Density profiles in open superdiffusive systems.
abstract: We numerically solve a discretized model of Lévy random walks on a finite one-dimensional domain with a reflection coefficient r and in the presence of sources. At the domain boundaries, the steady-state density profile is nonanalytic. The meniscus exponent μ, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that μ = α/2 + r(α/2 - 1), where α is the Lévy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain corresponds to a Lévy walk with negative reflection coefficient.
authors.affiliation: Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Lepri
authors.forename: Antonio
authors.initials: A
authors.lastname: Politi