International Centre for Theoretical Sciences, TIFR, Shivakote Village, Hesaraghatta Hobli, Bengaluru 560089, India.
Department of Physics, Keio University, Yokohama 223-8522, Japan.
Phys Rev Lett. 2018 Jun 1;120(22):220603. doi: 10.1103/PhysRevLett.120.220603.
A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.
最近基于涨落流体力学的理论预测，具有粒子、动量和能量守恒的一维相互作用系统表现出反常输运，可归入两个主要的普适类。该分类基于守恒量的平衡动力学相关性的行为。一类以具有 Kardar-Parisi-Zhang 标度的声波模式为特征，而第二类则具有扩散声波模式。热模式遵循 Lévy 统计，对于这两类有不同的指数。在这里，我们考虑了两个特定系统中的热流波动，预计它们处于上述两个普适类中，即具有哈密顿动力学的硬粒子气体和具有动量守恒随机动力学的调和链。数值模拟显示这两个系统中电流累积量的系统尺寸依赖性完全不同。我们使用来自涨落流体力学的 Lévy 漫步者的唯象模型来解释这一数值观察。这一致地解释了热流波动的系统尺寸依赖性。对于后一个系统，我们从更微观的理论推导出累积量生成函数，该理论也给出了累积量的相同系统尺寸依赖性。
