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Abstract <p>In this paper we consider two models of random walks on a random rough surface. In the first model the growth and fluctuations of the surface are modelled by Edwards–Wilkinson linear model, in second case they are modelled by non-linear Kardar–Parisi–Zhang equation. Despite the nonlinearity of the second model, ordinary perturbation theory gives us trivial critical dimensions and the only way to get non-trivial results is due to non-perturbative effects.</p>

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Random Walk on a Random Rough Surface: Renormalization Group Analysis of Two Models

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • N. V. Antonov,
  • N. M. Gulitskiy,
  • P. I. Kakin,
  • A. S. Romanchuk

摘要

Abstract

In this paper we consider two models of random walks on a random rough surface. In the first model the growth and fluctuations of the surface are modelled by Edwards–Wilkinson linear model, in second case they are modelled by non-linear Kardar–Parisi–Zhang equation. Despite the nonlinearity of the second model, ordinary perturbation theory gives us trivial critical dimensions and the only way to get non-trivial results is due to non-perturbative effects.