论文标题
公开设置中的随机平均转移过程中的质量波动
Mass fluctuations in Random Average Transfer Process in open set-up
论文作者
论文摘要
我们在每个站点的一维晶格上定义了一种新的质量运输模型。晶格与两端不同的“化学势”的质量储层连接。散装中的传质动力学等于在随机平均过程中粒子之间间隙的动力学。在非平衡稳态中，我们发现质量的多站点任意秩序累积物可以表示为$ 1/n $的膨胀，在每个顺序下，累积物都具有缩放形式。我们介绍了一种新颖的运算符方法，该方法使我们能够以$ 1/n $的不同订单来计算这些缩放功能。此外，这种方法表明，要完全表达高阶累积物的缩放函数，完全需要所有较低阶的多站点累积物。这与Wick的定理形成鲜明对比的是，所有高级累积物仅以两点累积剂表示。我们通过蒙特卡洛模拟的证据来支持我们的结果。
We define a new mass transport model on a one-dimensional lattice of size $N$ with continuous masses at each site. The lattice is connected to mass reservoirs of different `chemical potentials' at the two ends. The mass transfer dynamics in the bulk is equivalent to the dynamics of the gaps between particles in the Random Average Process. In the non-equilibrium steady state, we find that the multi-site arbitrary order cumulants of the masses can be expressed as an expansion in powers of $1/N$ where at each order the cumulants have a scaling form. We introduce a novel operator approach which allows us to compute these scaling functions at different orders of $1/N$. Moreover, this approach reveals that, to express the scaling functions for higher order cumulants completely one requires all lower order multi-site cumulants. This is in contrast to the Wick's theorem in which all higher order cumulants are expressed solely in terms of two-site cumulants. We support our results with evidence from Monte-Carlo simulations.
