Invited review: KPZ. Recent developments via a variational formulation
arXiv:1401.6425 · doi:10.4279/PIP.050010
Abstract
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 differential equation to be regarded as a gradient-flow counterpart to the KPZ equation. A dynamic renormalization group analysis at one-loop order of this new mesoscopic model yields the KPZ scaling relation alpha+z=2, as a consequence of the exact cancelation of the different 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 offers novel points of view and sheds light on particular aspects of the dynamics of the KPZ equation.
16 pages, 2 figures
References in corpus (12)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- An exact solution for the KPZ equation with flat initial conditions
- Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
- Numerical study of the Kardar-Parisi-Zhang equation
- On the Geometric Principles of Surface Growth
- Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
- Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth
- Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line
- Random-Manifold to Random-Periodic Depinning of an Elastic Interface
- Gauge fixing, BRS invariance and Ward identities for randomly stirred flows
- The universal high temperature regime of pinned elastic objects
- Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation