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Local average height distribution of fluctuating interfaces.

Naftali R Smith1, Baruch Meerson1, Pavel V Sasorov2

  • 1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.

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|February 18, 2017
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Summary
This summary is machine-generated.

Surface growth models face challenges with height distribution at higher dimensions. Introducing a local average height offers a well-defined alternative, revealing optimal interface paths and addressing UV catastrophe issues in models like KPZ.

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Area of Science:

  • Surface growth dynamics
  • Statistical physics
  • Nonlinear dynamics

Background:

  • Height fluctuations in growing surfaces are crucial for understanding surface growth phenomena.
  • The Kardar-Parisi-Zhang (KPZ) equation has shown significant progress in 1+1 dimensions.
  • Linear surface growth models face challenges with well-defined height distributions at critical dimensions.

Purpose of the Study:

  • To investigate the ill-defined nature of finite-time one-point height distributions in linear surface growth models at critical dimensions.
  • To introduce and analyze a local average height as a well-defined alternative for probability distributions.
  • To explore the implications for universality and optimal path determination in surface growth.

Main Methods:

  • Analysis of linear surface growth models, including the conserved and nonconserved Edwards-Wilkinson (EW) equations.
  • Introduction of a local average height to regularize ill-defined distributions.
  • Application of weak-noise theory to determine optimal interface paths conditioned on height fluctuations.
  • Investigation of the ultraviolet (UV) catastrophe in the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions.

Main Results:

  • Finite-time one-point height distributions are ill-defined in many linear models above critical dimensions without regularization.
  • Regularization via small-scale cutoffs can lead to a loss of universality.
  • The local average height provides a well-defined probability density in any dimension for linear models.
  • Optimal interface paths are determined for conditioned nonequilibrium fluctuations of the local average height.
  • The finite-time one-point height distribution in the nonregularized KPZ equation in 2+1 dimensions exhibits a UV catastrophe.

Conclusions:

  • A local average height is a viable and universal alternative for characterizing surface growth fluctuations in higher dimensions.
  • The study highlights the limitations of traditional height distribution methods and offers a path forward for complex systems.
  • Understanding optimal paths and potential catastrophes is crucial for predicting and controlling surface morphology.