Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel.
International Center for Theoretical Sciences, TIFR, Bangalore-560012, India.
Phys Rev E. 2019 Jan;99(1-1):012124. doi: 10.1103/PhysRevE.99.012124.
A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size L as ∼L^{-2/3} in the leading order with a diffusive correction of order ∼L^{-1}. The crossover length ℓ_{c} from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.
最近发展起来的非线性涨落流体力学理论在描述反常能量输运的各种特征方面非常成功。然而，该理论中的扩散项和噪声项不是从微观描述中推导出来的，而是从唯象学上添加的。在这里，我们通过在一维模型中对扩散项和噪声项进行显式计算，推导出这些流体力学方程。我们表明，在这个模型中，能量流在主导阶次上以 ∼L^{-2/3}的反常方式与系统尺寸 L 标度，并且有 ∼L^{-1}的扩散修正项。从扩散到反常输运的交叉长度 ℓ_{c}可以用微观参数表示。我们的理论预测得到了数值验证。
