Prosen Tomaz, Campbell David K
Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia.
Chaos. 2005 Mar;15(1):15117. doi: 10.1063/1.1868532.
We present analytic and numerical results on several models of one-dimensional (1D) classical lattices with the goal of determining the origins of anomalous heat transport and the conditions for normal transport in these systems. Some of the recent results in the literature are reviewed and several original "toy" models are added that provide key elements to determine which dynamical properties are necessary and which are sufficient for certain types of heat transport. We demonstrate with numerical examples that chaos in the sense of positivity of Lyapunov exponents is neither necessary nor sufficient to guarantee normal transport in 1D lattices. Quite surprisingly, we find that in the absence of momentum conservation, even ergodicity of an isolated system is not necessary for the normal transport. Specifically, we demonstrate clearly the validity of the Fourier law in a pseudo-integrable particle chain.
我们给出了关于一维（1D）经典晶格几种模型的解析和数值结果，目的是确定反常热输运的起源以及这些系统中正常输运的条件。回顾了文献中一些近期的结果，并添加了几个原始的“玩具”模型，这些模型提供了关键要素，以确定哪些动力学性质对于某些类型的热输运是必要的，哪些是充分的。我们通过数值例子表明，从李雅普诺夫指数为正的意义上讲，混沌对于保证一维晶格中的正常输运既不是必要的也不是充分的。非常令人惊讶的是，我们发现在没有动量守恒的情况下，即使是孤立系统的遍历性对于正常输运也不是必要的。具体而言，我们清楚地证明了傅里叶定律在一个准可积粒子链中的有效性。
