特邀评审:KPZ。通过变分公式的最新发展

IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY

Papers in Physics Pub Date : 2014-01-13 DOI:10.4279/PIP.050010

H. Wio, R. Deza, C. Escudero, J. Revelli

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引用次数: 6

摘要

最近，一种变分方法被引入到范式Kardar{Parisi{Zhang (KPZ)方程。在这里，我们回顾了这种方法，以及KPZ非平衡势(NEP)承认的泛函泰勒展开。这种展开在三阶处自然被截断，从而产生一个非线性随机偏微分方程，被视为与KPZ方程的梯度低对应物。在这个新的介观模型的一个环阶的动态重整化群分析得出KPZ比例关系+z = 2，作为顶点重整化的不同贡献的确切抵消的结果。考虑到这个方程的较低的对称性，特别是它不是伽利略不变量，这个结果是相当显著的。此外，利用该格式通过路径积分方法来查询KPZ方程的动力学行为。这些方面中的每一个都超越了新颖的观点，并阐明了KPZ方程动力学的特定方面。

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Invited review: KPZ. Recent developments via a variational formulation

Recently, a variational approach has been introduced for the paradigmatic Kardar{Parisi{ Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits. Such expansion becomes naturally truncated at third order, giving rise to a nonlinear stochastic partial dierential equation to be regarded as a gradient-ow counterpart to the KPZ equation. A dynamic renormalization group analysis at one-loop order of this new mesoscopic model yields the KPZ scaling relation +z = 2, as a consequence of the exact cancelation of the dierent contributions to vertex renormalization. This result is quite remarkable, considering the lower degree of symmetry of this equation, which is in particular not Galilean invariant. In addition, this scheme is exploited to inquire about the dynamical behavior of the KPZ equation through a path-integral approach. Each of these aspects oers novel points of view and sheds light on particular aspects of the dynamics of the KPZ equation.

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来源期刊

Papers in Physics PHYSICS, MULTIDISCIPLINARY-

CiteScore

1.90

自引率

0.00%

发文量

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