Interface models

Transient dynamics in the Edwards-Wilkinson model

We study the Langevin dynamics of an interface within the Edwards-Wilkinson model (or equivalently  the Rouse chain model for a polymer). We develope a functional Fokker-Planck approach in order to study the effect of pinning of a single monomer and the effect of killing of the monomer (absorption).

pinned-edwards-wilkinson

 

Distribution of the center of mass of interfaces

We consider a model of Brownian N non intersecting interfaces with a repulsive substrate. Nadal & Majumdar [Phys. Rev. E 79, 061117 (2009)] have studied the distribution of the position of the highest interface, h1, and also the distribution of the center of mass G=(1/Ni=1N hi.

schema_interf

In this article we consider the distribution of the fraction κ=N1/N of top interfaces. Using a mapping on a random matrix problem (within the Laguerre ensemble) we are led to study the distribution of a truncated linear statistics of the eigenvalues of Wishart matrices.

See also page  “ Random matrix theory

 

Counting equilibria for a directed polymer in a random environment

At T=0, an elastic line in a disordered medium submitted to a uniform force field is pinned by the disorder for a force below a critical threshold fc. We consider this problem by studying the average number of equilibria (stable or unstable).

niceline-big

  • Yan V. Fyodorov, Pierre Le Doussal, Alberto Rosso and Christophe Texier,
    Exponential number of equilibria and depinning threshold for a directed polymer in a random potential,
    cond-mat.dis-nn arXiv:1703.10066

Les commentaires sont fermés.