Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2+1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we return here to study, in depth, the three-dimensional (3D) radial KPZ problem, comparing common scaling phenomena exhibited by the pt-pt directed polymer in a random medium (DPRM), the stochastic heat equation (SHE) with multiplicative noise ...

The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that associated with the KPZ equation. A feature common to these studies is the presence of holes (bubbles and overhangs) in the bulk and an interface that is smeared out....

Motivated by the recent exact solution of the stationary-state Kardar-Parisi-Zhang (KPZ) statistics by Imamura and Sasamoto [ Phys. Rev. Lett. 108 190603 (2012)], as well as a precursor experimental signature unearthed by Takeuchi [ Phys. Rev. Lett. 110 210604 (2013)], we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the...

Citation: Wio HS, Rodríguez MA, Gallego R, Revelli JA, Alés A and Deza RR (2017) d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional. Front. Phys. 4:52. doi: 10.3389/fphy.2016.00052 d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of I...

A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar–Parisi–Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or high...

We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary proba...

We consider the narrow wedge solution to Kardar–Parisi–Zhang stochastic PDE under characteristic 3:2:1 scaling of time, space and fluctuations. study correlation fluctuations at two different times. show that, when times are close each other, approaches one a power-law rate with exponent 2/3, while, remote from tends zero ?1/3. also prove exponential-type tail bounds for differences space-time ...