Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model

Tadahisa Funaki, H. Spohn

Research output: Contribution to journalArticle

83 Citations (Scopus)

Abstract

We consider the scalar field φt with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy ∫ ddxV(▽φ(x)). The potential V is even and strictly convex. We prove that under a suitable large scale limit the φt-field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the ▽φ-field.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalCommunications in Mathematical Physics
Volume185
Issue number1
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Motion by Mean Curvature
Gibbs Measure
Ginzburg-Landau
curvature
Ergodic Measure
Dirichlet Form
Stochastic Dynamics
Strictly Convex
Tilt
Mean Curvature
Scalar Field
Anisotropy
Directly proportional
scalars
anisotropy
Invariant
shift
Energy
Model
energy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model. / Funaki, Tadahisa; Spohn, H.

In: Communications in Mathematical Physics, Vol. 185, No. 1, 1997, p. 1-36.

Research output: Contribution to journalArticle

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