### Abstract

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spatial dimensionality of the system. In the special case of Edwards-Wilkinson growth, our mean field theory correctly reproduces all features. In the presence of a nonlinear term one observes a crossover to a KPZ-like behaviour with the correct dynamical exponent z = 3/2. In particular we compute the skewed interface profile during roughening, and we study the influence of a co-moving reflecting wall, which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions. Also here the mean field approximation reproduces all qualitative features of the full KPZ equation, although with different values of the surface exponents.

Original language | English |
---|---|

Pages (from-to) | 11085-11100 |

Number of pages | 16 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 46 |

DOIs | |

Publication status | Published - 19 Nov 2004 |

### Keywords

- directed polymers
- multiplicative noise
- critical-behavior
- random matrices
- universality
- dimensions
- interfaces
- invariance
- equation
- systems

### Cite this

*Journal of Physics A: Mathematical and General*,

*37*(46), 11085-11100. https://doi.org/10.1088/0305-4470/37/46/001

**Mean field theory for skewed height profiles in KPZ growth.** / Ginelli, Francesco Giulio; Hinrichsen, Haye.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 37, no. 46, pp. 11085-11100. https://doi.org/10.1088/0305-4470/37/46/001

}

TY - JOUR

T1 - Mean field theory for skewed height profiles in KPZ growth

AU - Ginelli, Francesco Giulio

AU - Hinrichsen, Haye

PY - 2004/11/19

Y1 - 2004/11/19

N2 - We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spatial dimensionality of the system. In the special case of Edwards-Wilkinson growth, our mean field theory correctly reproduces all features. In the presence of a nonlinear term one observes a crossover to a KPZ-like behaviour with the correct dynamical exponent z = 3/2. In particular we compute the skewed interface profile during roughening, and we study the influence of a co-moving reflecting wall, which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions. Also here the mean field approximation reproduces all qualitative features of the full KPZ equation, although with different values of the surface exponents.

AB - We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spatial dimensionality of the system. In the special case of Edwards-Wilkinson growth, our mean field theory correctly reproduces all features. In the presence of a nonlinear term one observes a crossover to a KPZ-like behaviour with the correct dynamical exponent z = 3/2. In particular we compute the skewed interface profile during roughening, and we study the influence of a co-moving reflecting wall, which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions. Also here the mean field approximation reproduces all qualitative features of the full KPZ equation, although with different values of the surface exponents.

KW - directed polymers

KW - multiplicative noise

KW - critical-behavior

KW - random matrices

KW - universality

KW - dimensions

KW - interfaces

KW - invariance

KW - equation

KW - systems

U2 - 10.1088/0305-4470/37/46/001

DO - 10.1088/0305-4470/37/46/001

M3 - Article

VL - 37

SP - 11085

EP - 11100

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 46

ER -