Le Doussal Pierre, Thiery Thimothée
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Cedex 05 Paris, France.
Instituut voor Theoretische Fysica, KU Leuven, 3001 Leuven, Belgium.
Phys Rev E. 2017 Jul;96(1-1):010102. doi: 10.1103/PhysRevE.96.010102. Epub 2017 Jul 10.
Although time-dependent random media with short-range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in one-dimensional (1D) lattice random walks, where statistics related to the 1D Kardar-Parisi-Zhang (KPZ) universality class, i.e., the Gaussian unitary ensemble Tracy-Widom distribution, were shown to arise. Here, we provide a simple picture for this correspondence, directly in the continuum, which allows one to study arbitrary space dimensions and to predict a variety of universal distributions. In d=1, we predict and verify numerically the emergence of the Gaussian orthogonal ensemble Tracy-Widom distribution for fluctuations of the transition probability. In d=3, we predict a phase transition from Gaussian fluctuations to three-dimensional KPZ-type fluctuations as the bias is increased. We predict KPZ universal distributions for the arrival time of a first particle from a cloud diffusing in such media.
尽管具有短程相关性的时间相关随机介质会导致（可能有偏差的）正常示踪剂扩散，但在远离最可能方向时会出现异常涨落。这一点最近在一维（1D）晶格随机游走中被指出，其中与一维 Kardar-Parisi-Zhang（KPZ）普适类相关的统计量，即高斯酉系综 Tracy-Widom 分布，已被证明会出现。在此，我们直接在连续统中为这种对应关系提供一个简单的图景，这使得人们能够研究任意空间维度并预测各种普适分布。在 d = 1 时，我们预测并通过数值验证了转移概率涨落的高斯正交系综 Tracy-Widom 分布的出现。在 d = 3 时，我们预测随着偏差增加会出现从高斯涨落到三维 KPZ 型涨落的相变。我们预测了在这种介质中扩散的云团中第一个粒子到达时间的 KPZ 普适分布。
