Dynamical phase transition for current statistics in a simple driven diffusive system
Dynamical phase transition for current statistics in a simple driven diffusive system
复制标题
简单驱动扩散系统中电流统计的动态相变
DOI：
10.1103/physreve.87.032115
复制
发表时间：
2012
影响因子：
2.4
通讯作者：
P. Hurtado
中科院分区：
文献类型：
--
作者：
Carlos P. Espigares;P. Garrido;P. Hurtado
我们考虑环上一维弱不对称排斥过程中时间平均电流的波动。维持给定波动的最佳密度分布对于足够低的电流表现出不稳定性，其中它变得与时间相关。这种不稳定性对应于系统波动行为中的动态相变：虽然典型的电流波动是由弱相关局部事件的总和产生的，并且仍然与平坦的稳态密度分布相关，但对于低于临界阈值的电流，系统以相干行波的形式自组织成宏观堵塞状态，这阻碍了粒子的传输，从而促进了远低于平均电流的时间平均电流波动。我们使用先进的蒙特卡罗模拟详细分析了这种现象，并制定了宏观波动理论预测，在所有情况下都发现了非常好的一致性。特别是，我们不仅研究电流大偏差函数，还研究临界电流阈值、相关的最佳密度分布和行波速度，深入分析有限尺寸效应，从而提供动态过渡的详细表征。
We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.