论文标题
超扩散和从扩散到一维系统中异常运输的交叉
Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
论文作者
论文摘要
我们研究具有两个保守量的一维晶格系统的运输 - “体积”和能量。考虑到一个缓慢发展的局部平衡状态，该状态略微偏离了潜在的全局平衡，我们估计校正对局部平衡分布。这种校正主要通过某些局部电流的时空相关性产生。在连续限制中，我们表明，局部平衡分布以及校正的“体积”的漂移扩散方程和线性响应状态中能量的超扩散方程，因为宏观流体动力学将从非线性波动流体动力学理论中获得。我们发现超扩散方程的明确表达。此外，我们发现对超扩散演化的扩散校正。这样的校正使我们能够研究从扩散到异常运输的跨界。我们通过在平衡中的最初局部热脉冲以及通过非平衡稳态稳定电流的系统尺寸尺度扩散来证明这一交叉。
We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the `volume' and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.
