title: Watersheds are Schramm-Loewner evolution curves.
abstract: We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE(κ), with κ = 1.734 ± 0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c ≈ -7/2.
authors.affiliation: Computational Physics for Engineering Materials, Institut f. Baustoffe, ETH Zurich, Wolfgang-Pauli-Street 27, 8093 Zurich, Switzerland. daryaei@physics.sharif.edu
authors.forename: E
authors.initials: E
authors.lastname: Daryaei
authors.forename: N A M
authors.initials: NA
authors.lastname: Araújo
authors.forename: K J
authors.initials: KJ
authors.lastname: Schrenk
authors.forename: S
authors.initials: S
authors.lastname: Rouhani
authors.forename: H J
authors.initials: HJ
authors.lastname: Herrmann