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Exact result vs. dynamic renormalization group analysis for the non-local Kardar–Parisi–Zhang equation

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  • Katzav, Eytan

Abstract

In this paper I discuss a generalization of the well-known Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions. This Non-local Kardar–Parisi–Zhang (NKPZ) equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of colloids. I show that the steady state strong coupling solution for a subfamily of the NKPZ models can be solved exactly in one dimension, using the Fokker–Planck form of the equation, and yields a Gaussian distribution. This exact result does not agree with a previous result obtained by dynamic renormalization group (DRG) analysis. The reasons for this disagreement are not yet clear.

Suggested Citation

  • Katzav, Eytan, 2002. "Exact result vs. dynamic renormalization group analysis for the non-local Kardar–Parisi–Zhang equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 79-84.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:1:p:79-84
    DOI: 10.1016/S0378-4371(02)00597-6
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    Cited by:

    1. Katzav, Eytan, 2013. "Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1750-1755.
    2. Lu, Xinyu & Hao, Dapeng & Xia, Hui, 2022. "Kinetic roughening in the nonlocal Kardar–Parisi–Zhang growth: Pseudospectral versus finite difference schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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