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Polymer dynamics in the depinned phase: metastability with logarithmic barriers
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  • Published: 17 March 2011

Polymer dynamics in the depinned phase: metastability with logarithmic barriers

  • Pietro Caputo1,
  • Hubert Lacoin1,
  • Fabio Martinelli1,
  • François Simenhaus1 &
  • …
  • Fabio Lucio Toninelli2 

Probability Theory and Related Fields volume 153, pages 587–641 (2012)Cite this article

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Abstract

We consider the stochastic evolution of a (1 + 1)-dimensional polymer in the depinned regime. At equilibrium the system exhibits a double well structure: the polymer lies (essentially) either above or below the repulsive line. As a consequence, one expects a metastable behavior with rare jumps between the two phases combined with a fast thermalization inside each phase. However, the energy barrier between these two phases is only logarithmic in the system size L and therefore the two relevant time scales are only polynomial in L with no clear-cut separation between them. The whole evolution is governed by a subtle competition between the diffusive behavior inside one phase and the jumps across the energy barriers. Our main results are: (i) a proof that the mixing time of the system lies between \({L^{\frac 5 2}}\) and \({L^{\frac 5 2 +2}}\) ; (ii) the identification of two regions associated with the positive and negative phase of the polymer together with the proof of the asymptotic exponentiality of the tunneling time between them with rate equal to a half of the spectral gap.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università Roma Tre, Largo S. Murialdo 1, 00146, Rome, Italy

    Pietro Caputo, Hubert Lacoin, Fabio Martinelli & François Simenhaus

  2. CNRS and ENS Lyon, Laboratoire de Physique, 46 Allée d’Italie, 69364, Lyon, France

    Fabio Lucio Toninelli

Authors
  1. Pietro Caputo
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  2. Hubert Lacoin
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  3. Fabio Martinelli
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  4. François Simenhaus
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  5. Fabio Lucio Toninelli
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Corresponding author

Correspondence to Fabio Martinelli.

Additional information

This work was supported by the European Research Council through the “Advanced Grant” PTRELSS 228032.

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Cite this article

Caputo, P., Lacoin, H., Martinelli, F. et al. Polymer dynamics in the depinned phase: metastability with logarithmic barriers. Probab. Theory Relat. Fields 153, 587–641 (2012). https://doi.org/10.1007/s00440-011-0355-6

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  • Received: 26 July 2010

  • Revised: 04 March 2011

  • Published: 17 March 2011

  • Issue Date: August 2012

  • DOI: https://doi.org/10.1007/s00440-011-0355-6

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Keywords

  • Reversible Markov chains
  • Polymer pinning model
  • Metastability
  • Spectral gap
  • Mixing time
  • Coupling
  • Quasi-stationary distribution

Mathematics Subject Classification (2000)

  • 60K35
  • 82C20
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