Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany.
Department of Mathematics and Department of Physics and Astronomy, Purdue University, 150 North University Street, West Lafayette, Indiana 47906, USA.
Phys Rev E. 2017 Sep;96(3-1):032119. doi: 10.1103/PhysRevE.96.032119. Epub 2017 Sep 13.
We define a stochastic lattice model for a fluctuating directed polymer in d≥2 dimensions. This model can be alternatively interpreted as a fluctuating random path in two dimensions, or a one-dimensional asymmetric simple exclusion process with d-1 conserved species of particles. The deterministic large dynamics of the directed polymer are shown to be given by a system of coupled Kardar-Parisi-Zhang (KPZ) equations and diffusion equations. Using nonlinear fluctuating hydrodynamics and mode coupling theory we argue that stationary fluctuations in any dimension d can only be of KPZ type or diffusive. The modes are pure in the sense that there are only subleading couplings to other modes, thus excluding the occurrence of modified KPZ-fluctuations or Lévy-type fluctuations, which are common for more than one conservation law. The mode-coupling matrices are shown to satisfy the so-called trilinear condition.
我们定义了一个在 d≥2 维空间中波动的定向聚合物的随机格点模型。这个模型可以被解释为二维空间中的波动随机路径，或者一维的非对称简单排斥过程，其中有 d-1 种守恒的粒子。定向聚合物的确定性大动力学由一组耦合的 Kardar-Parisi-Zhang (KPZ) 方程和扩散方程给出。我们利用非线性随机流体力学和模式耦合理论，证明了在任何维度 d 中，稳定的波动只能是 KPZ 类型或扩散类型。这些模式是纯粹的，因为它们只有次要的与其他模式的耦合，从而排除了发生修正的 KPZ 波动或 Lévy 类型波动的可能性，这些波动在超过一个守恒定律的情况下很常见。模式耦合矩阵被证明满足所谓的三线性条件。
