Computational Physics for Engineering Materials, Institut f. Baustoffe, ETH Zurich, Wolfgang-Pauli-Street 27, 8093 Zurich, Switzerland.
Phys Rev Lett. 2012 Nov 21;109(21):218701. doi: 10.1103/PhysRevLett.109.218701. Epub 2012 Nov 20.
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.
我们证明，在连续统极限下水系划分流域是 Schramm-Loewner 演化（SLE）曲线，由单个参数 κ 描述。我们进行了多次数值评估以确定这一点。所有的计算都与 SLE(κ)一致，κ=1.734±0.005，这是κ<2 的 SLE 中已知的唯一物理实例。这超出了著名的对偶猜想，引发了关于对偶模型存在性和可逆性的新问题。此外，这强烈表明在随机景观中存在共形不变性，并表明分水岭可能对应于具有中心电荷 c≈-7/2 的对数共形场论。
