University Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France.
Phys Rev E. 2019 Dec;100(6-1):062143. doi: 10.1103/PhysRevE.100.062143.
We investigate the universal behavior of the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise. The presence of time correlations in the microscopic noise breaks the statistical tilt symmetry, or Galilean invariance, of the original KPZ equation with δ-correlated noise (denoted SR-KPZ). Thus, it is not clear whether the KPZ universality class is preserved in this case. Conflicting results exist in the literature, some advocating that it is destroyed even in the limit of infinitesimal temporal correlations, while others find that it persists up to a critical range of such correlations. Using nonperturbative and functional renormalization group techniques, we study the influence of two types of temporal correlators of the noise: a short-range one with a typical timescale τ, and a power-law one with a varying exponent θ. We show that for the short-range noise with any finite τ, the symmetries (the Galilean symmetry, and the time-reversal one in 1+1 dimension) are dynamically restored at large scales, such that the long-distance and long-time properties are governed by the SR-KPZ fixed point. In the presence of a power-law noise, we find that the SR-KPZ fixed point is still stable for θ below a critical value θ_{th}, in accordance with previous renormalization group results, while a long-range fixed point controls the critical scaling for θ>θ_{th}, and we evaluate the θ-dependent critical exponents at this long-range fixed point, in both 1+1 and 2+1 dimensions. While the results in 1+1 dimension can be compared with previous studies, no other prediction was available in 2+1 dimension. We finally report in 1+1 dimension the emergence of anomalous scaling in the long-range phase.
我们研究了具有时相关噪声的 Kardar-Parisi-Zhang（KPZ）方程的普遍行为。微观噪声中的时相关打破了具有 δ 相关噪声的原始 KPZ 方程（表示为 SR-KPZ）的统计倾斜对称性或伽利略不变性。因此，在这种情况下，KPZ 普遍性是否得以保留尚不清楚。文献中存在相互矛盾的结果，一些人认为即使在微小的时相关的极限下，它也会被破坏，而另一些人则发现它在这种相关的临界范围内仍然存在。我们使用非微扰和泛函重整化群技术研究了噪声的两种时相关器的影响：具有典型时间尺度 τ 的短程相关器和具有变化指数 θ 的幂律相关器。我们表明，对于具有任何有限 τ 的短程噪声，在大尺度下，对称性（伽利略对称性和 1+1 维中的时间反演对称性）被动态恢复，使得长距离和长时间特性由 SR-KPZ 不动点控制。在存在幂律噪声的情况下，我们发现对于 θ 低于临界值 θ_{th}，SR-KPZ 不动点仍然稳定，这与之前的重整化群结果一致，而对于 θ>θ_{th}，长程固定点控制着临界标度，我们在这一长程固定点处评估了 θ 相关的临界指数，在 1+1 和 2+1 维度上均如此。虽然 1+1 维度上的结果可以与以前的研究进行比较，但在 2+1 维度上没有其他预测。我们最后在 1+1 维度上报告了长程相中的异常标度出现。
