Universal fluctuations in Kardar-Parisi-Zhang growth on one-dimensional flat substrates

Oliveira, Tiago J.; Ferreira, Silvio C.; Alves, Sidiney G.

doi:10.1103/physreve.85.010601

Cited by 43 publications

(59 citation statements)

References 29 publications

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“…This section presents numerical results for one-dimensional enlarging substrates, with ω = L 0 and up to 25 000 realizations. Figure 2 [7,15,20,33]. Our results indeed underpin this finite-time correction, and, extrapolating the data, we find that the asymptotic skewness and kurtosis indicate the values for the GUE TW distribution.…”

Section: Height Fluctuations In 1 +1 Dimensionssupporting

confidence: 70%

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Interface fluctuations for deposition on enlarging flat substrates

2014

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We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In 1 + 1 dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy 2 process instead of the GOE and Airy 1 foreseen for flat interfaces. These results imply that when the KPZ class splits into curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than, the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in 2 + 1 dimensions, the analog of the GUE Tracy-Widom distribution for height distribution and that of the Airy 2 process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated with the duplication of columns is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.

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Section: Height Fluctuations In 1 +1 Dimensionssupporting

confidence: 70%

“…. Following the same procedures as in [19,20], we found = ∞ v 2.13986 (5) and Γ = 4.90(9) for the etching model. All these results were obtained for ω = 0, but the validity of these values for the expanding case was explicitly verified.…”

Section: Height Fluctuations In 1 +1 Dimensionsmentioning

confidence: 71%

Interface fluctuations for deposition on enlarging flat substrates

2014

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“…The comparison of the distributions of scanned surfaces at different times with KPZ can be seen in figure 3, showing that the results are visually robust withing this time window. One interesting feature observed for MBE is that the skewness initially approaches the KPZ value = S 0.43 KPZ as time increases in analogy with the finitetime corrections observed in experiments [11,14,48] and simulations [13,17,39,49] of actual KPZ systems. For example, the skewness of the height distributions in MBE are = S 0.55, 0.49, 0.45, and 0.41 for = t 50, 100, 200 and 500 but, differently from actual KPZ systems, it keeps decreasing and start to deviate considerably from KPZ for longer times.…”

Section: Spm Surfaces and The Kpz Classsupporting

confidence: 54%

Hallmarks of the Kardar–Parisi–Zhang universality class elicited by scanning probe microscopy

2016

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Scanning probe microscopy is a fundamental technique for the analysis of surfaces. In the present work, the interface statistics of surfaces scanned with a probe tip is analyzed for both in silico and experimental systems that, in principle, do not belong to the prominent Kardar-Parisi-Zhang universality class. We observe that some features such as height, local roughness and extremal height distributions of scanned surfaces quantitatively agree with the KPZ class with good accuracy. The underlying mechanism behind this artifactual KPZ class is the finite size of the probe tip, which does not permit a full resolution of neither deep valleys nor sloping borders of plateaus. The net result is a scanned profile laterally thicker and higher than the original one implying an excess growth, a major characteristic of the KPZ universality class. Our results are of relevance whenever either the normal or lateral characteristic lengths of the surface are comparable with those of the probe tip. Thus our finds can be relevant, for example, in experiments where sufficiently long growth times cannot be achieved or in mounded surfaces with high aspect ratio.

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“…(1)], Γ is a nonuniversal constant associated to the amplitude of the interface fluctuations, β is the growth exponent, and χ is a stochastic quantity given by Tracy-Widom [13] distributions. This conjecture was confirmed in distinct KPZ systems [14][15][16][17][18][19] besides exact solutions of KPZ equation [20][21][22][23]. Recent numerical simulations have shown that the KPZ ansatz can be generalized to 2+1 [24][25][26] and higher [27] dimensions, but the exact forms of the asymptotic distributions of χ are yet not known.…”

Section: Introductionmentioning

confidence: 89%

Origins of scaling corrections in ballistic growth models

2014

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We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtained scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in divide the surface in bins of size ε and use only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class were found. The binning method allowed the accurate determination of the height distributions of the ballistic models in both growth and steady state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in 2 + 1 dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.

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Universal fluctuations in Kardar-Parisi-Zhang growth on one-dimensional flat substrates

Cited by 43 publications

References 29 publications

Interface fluctuations for deposition on enlarging flat substrates

Interface fluctuations for deposition on enlarging flat substrates

Hallmarks of the Kardar–Parisi–Zhang universality class elicited by scanning probe microscopy

Origins of scaling corrections in ballistic growth models

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