Popkov Vladislav, Schadschneider Andreas, Schmidt Johannes, Schütz Gunter M
Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany; Centro Interdipartimentale per lo Studio di Dinamiche Complesse, Università di Firenze, 50019 Sesto Fiorentino, Italy;
Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany;
Proc Natl Acad Sci U S A. 2015 Oct 13;112(41):12645-50. doi: 10.1073/pnas.1512261112. Epub 2015 Sep 30.
Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.
普遍性是平衡态物理学中一个已确立的核心概念。然而，在远离平衡态的系统中，对其基本原理仍缺乏更深入的理解。到目前为止，已经确定了几类。除了具有动力学指数[公式：见正文]的扩散普遍性类之外，另一个突出的例子是具有[公式：见正文]的超扩散 Kardar-Parisi-Zhang（KPZ）类。例如，它出现在远离热平衡且表现出某些守恒定律的低维动力学现象中。在这里，我们表明这两类都只是非平衡普遍性类的无限离散族的一部分。值得注意的是，它们的动力学指数[公式：见正文]由相邻斐波那契数的比值给出，要么从[公式：见正文]开始（如果存在 KPZ 模式），要么从[公式：见正文]开始（如果存在扩散模式）。如果既不存在扩散模式也不存在 KPZ 模式，那么所有动力学模式都具有黄金分割比[公式：见正文]作为动力学指数。这些斐波那契模式的通用标度函数是不对称的 Lévy 分布，它们完全由系统的宏观电流密度关系和压缩性矩阵确定，因此可以通过实验测量得到。
