| | |
| | |
Stat |
Members: 3645 Articles: 2'504'928 Articles rated: 2609
25 April 2024 |
|
| | | |
|
Article overview
| |
|
On the approach to equilibrium for a polymer with adsorption and repulsion | Pietro Caputo
; Fabio Martinelli
; Fabio Lucio Toninelli
; | Date: |
17 Sep 2007 | Abstract: | We consider paths of a one-dimensional simple random walk conditioned to come
back to the origin after L steps (L an even integer). In the ’pinning model’
each path eta has a weight lambda^{N(eta)}, where lambda>0 and N(eta) is
the number of zeros in eta. When the paths are constrained to be non-negative,
the polymer is said to satisfy a hard-wall constraint. Such models are well
known to undergo a localization/delocalization transition as the pinning
strength lambda is varied. In this paper we study a natural ’spin flip’
dynamics for these models and derive several estimates on its spectral gap and
mixing time. In particular, for the system with the wall we prove that
relaxation to equilibrium is always at least as fast as in the free case
(lambda=1, no wall), where the gap and the mixing time are known to scale as
L^{-2} and L^2log L, respectively. This improves considerably over previously
known results. For the system without the wall we show that the equilibrium
phase transition has a clear dynamical manifestation: for lambda geq 1 the
relaxation is again at least as fast as the diffusive free case, but in the
strictly delocalized phase (lambda < 1) the gap is shown to be O(L^{-5/2}), up
to logarithmic corrections. As an application of our bounds, we prove stretched
exponential relaxation of local functions in the localized regime. | Source: | arXiv, 0709.2612 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |