Metastability for Ginzburg Landau type

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Niveau: Supérieur
Metastability for Ginzburg-Landau-type SPDEs with space-time white noise Nils Berglund MAPMO, Universite d'Orleans CNRS, UMR 6628 and Federation Denis Poisson Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, Universite de Bielefeld Bielefeld, 19 November 2009

  • configuration space

  • transition path

  • free energy

  • full configuration

  • stochastic lattice

  • order parameter

  • µ?

  • supersaturated gas

  • gibbs measure


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Metastability for Ginzburg-Landau-type
SPDEs
with space-time white noise
Nils Berglund MAPMO,Universit´edOrl´eans CNRS,UMR6628andFe´de´rationDenisPoisson www.univ-orleans.fr/mapmo/membres/berglund
Collaborators: Florent Barret , Ecole Polytechnique, Palaiseau Bastien Fernandez , CPT, CNRS, Marseille Barbara Gentz ,Universit´edeBielefeld
Bielefeld, 19 November 2009
Metastability in
Examples:
Supercooled
physics
liquid
Supersaturated gas
Wrongly
magnetised
ferromagnet
1
Metastability in physics
Examples:
Supercooled liquid Supersaturated gas Wrongly magnetised ferromagnet
. Near first-order phase transition . Nucleation implies crossing energy
barrier
1-a
Metastability in stochastic lattice models
.aLttice:Λ
Z d . Configuration space: X = S Λ , S finite set (e.g. {− 1 , 1 } ) . Hamiltonian: H : X → R (e.g. Ising or lattice gas) . Gibbs measure: µ β ( x ) = e βH ( x ) /Z β . Dynamics: Markov chain with invariant measure µ β (e.g. Metropolis: Glauber or Kawasaki)
2