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).
- Shamik Gupta, Alberto Rosso and Christophe Texier,
Dynamics of a tagged monomer: Effects of elastic pinning and harmonic absorption
Phys. Rev. Lett. 111, 210601 (2013)
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/N)Σi=1N hi.
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.
- Aurélien Grabsch, Satya N. Majumdar and Christophe Texier,
Truncated linear statistics associated with the top eigenvalues of random matrices ,
J. Stat. Phys. 167(2), 234-259 (2017)
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).
- 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,