Kinetic roughening, global quantities, and fluctuation–dissipation relations

Chou, Yen-Liang; Pleimling, Michel

doi:10.1016/j.physa.2012.02.022

Cited by 7 publications

(13 citation statements)

References 29 publications

(69 reference statements)

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“…A relation equivalent to Eq. (8) is also obtained for the squared local curvature of the MH equation with y = 1/4 in d = 1 (again, a small correction exponent) [34].…”

Section: Results In D =mentioning

confidence: 66%

“…For the linear EW and MH equations in d = 1, the López approach actually predicts the correct values κ = −1/4 and 1/8, respectively (the former corresponding to y = 1/2 in our notation) [33,34]. However, that approach is not exact for nonlinear models.…”

Section: Discussionmentioning

confidence: 87%

“…This exponent decreases as d decreases in all cases in which it can be exactly calculated. For instance, in d = 1, the KPZ class has y = 2/3 and the EW class has y = 1/2, while in d = 2 the respective values are 0.76 and 1 [33,34]. A relation equivalent to Eq.…”

Section: Results In D =mentioning

confidence: 99%

“…Typical examples are EdwardsWilkinson (EW) [31] and Kardar-Parisi-Zhang (KPZ) [32] growth, respectively, with y = d/2 and y = 2 (1 − α) /z [33,34] (in the original work of Krug and Meakin [33], the exponent y is denoted α ⊥ ).…”

Section: A Roughness Correlation Function and Dynamic Scalingmentioning

confidence: 99%

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Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

Reis

2013

Phys. Rev. E

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The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions d=1 and 2. In d=1, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to 0.1. Other VLDS models in d=1, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to 10(6) monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In d=2, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in d=1 and 2, in agreement with the theoretical predictions of Phys. Rev. Lett. 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.

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“…A relation equivalent to Eq. (8) is also obtained for the squared local curvature of the MH equation with y = 1/4 in d = 1 (again, a small correction exponent) [34].…”

Section: Results In D =mentioning

confidence: 66%

Section: Discussionmentioning

confidence: 87%

Section: Results In D =mentioning

confidence: 99%

Section: A Roughness Correlation Function and Dynamic Scalingmentioning

confidence: 99%

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Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

Reis

2013

Phys. Rev. E

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“…In the context of interfaces, the fluctuations of a two-time quantity the average of which is the roughness were studied in [23][24][25][26]. The Fourier transformed noise statistics are such that ξ( k, t) = 0 and ξ( k,…”

Section: The Free Scalar Fieldmentioning

confidence: 99%

Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz–Thouless phase

Corberi

Cugliandolo

2012

J. Stat. Mech.

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We study analytically the distribution of fluctuations of the quantities whose average yield the usual two-point correlation and linear response functions in three unfrustrated models: the random walk, the d dimensional scalar field and the 2d XY model. In particular we consider the time dependence of ratios between composite operators formed with these fluctuating quantities which generalize the largely studied fluctuation-dissipation ratio, allowing us to discuss the relevance of the effective temperature notion beyond linear order. The behavior of fluctuations in the aforementioned solvable cases is compared to numerical simulations of the 2d clock model with p = 6, 12 states. Contents

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Field-Theoretic Thermodynamic Uncertainty Relation

2020

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We propose a field-theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the one-dimensional Kardar-Parisi-Zhang equation, a paradigmatic example of a non-linear field-theoretic Langevin equation. In particular, we will treat the dimensionless Kardar-Parisi-Zhang equation with an effective coupling parameter measuring the strength of the non-linearity. It will be shown that a field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the field-theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the Kardar-Parisi-Zhang equation due to an excess term stemming from its non-linearity.

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Kinetic roughening, global quantities, and fluctuation–dissipation relations

Cited by 7 publications

References 29 publications

Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz–Thouless phase

Field-Theoretic Thermodynamic Uncertainty Relation

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