体驱动迁移模型大偏差泛函的奇异性
Singularities in Large Deviation Functionals of Bulk-Driven Transport Models
摘要：
采用数值和解析相结合的方法研究了开边界弱非对称排斥过程密度场的大偏差泛函。对于适当的边界条件和批量驱动器的功能变得不可微。这种情况发生在配置，而不是一个单一的历史，几个不同的历史等权重主导其动态演化。正如我们所展示的，奇点的结构可以相当丰富。我们确定在一个临界点和类似物的三临界点结束的一阶相变线的配置空间中的数值模拟。一阶线终止于临界点时，出现的配置，其动力学演化是由两个不同的历史具有相同的权重控制。三临界点类似物出现时，有配置的动力学演化是由三个不同的历史控制的重量相同。数值分析表明，奇异结构可以用朗道理论描述。最后，在一个无限大的偏见的限制，我们确定奇点所产生的竞争s的历史，与s任意。在这种情况下，我们表明，所有的奇点可以描述的朗道一样的理论。
英文摘要：
The large deviation functional of the density field in the weakly asymmetric exclusion process with open boundaries is studied using a combination of numerical and analytical methods. For appropriate boundary conditions and bulk drives the functional becomes non-differentiable. This happens at configurations where instead of a single history, several distinct histories of equal weight dominate their dynamical evolution. As we show, the structure of the singularities can be rather rich. We identify numerically analogues in configuration space of first order phase transition lines ending at a critical point and analogues of tricritical points. First order lines terminating at a critical point appear when there are configurations whose dynamical evolution is controlled by two distinct histories with equal weight. Tricritical point analogues emerge when there are configurations whose dynamical evolution is controlled by three distinct histories with equal weight. A numerical analysis suggests that the structure of the singularities can be described by a Landau like theory. Finally, in the limit of an infinite bulk bias we identify singularities which arise from a competition of s histories, with s arbitrary. In this case we show that all the singularities can be described by a Landau like theory.
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