Localization of Polymers in Random Media: Analogy with Quantum Particles in Disorder
| dc.creator | Goldschmidt, Yadin Y. | |
| dc.creator | Shiferaw, Yohannes | |
| dc.date | 2004-11-08 | |
| dc.date.accessioned | 2026-07-07T03:01:56Z | |
| dc.date.available | 2026-07-07T03:01:56Z | |
| dc.description | In this chapter we review the rich behavior of polymer chains embedded in a quenched random environment. We first consider the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derive the equilibrium conformation of the chain using a replica variational ansatz, and highlight the crucial role of the system's volume. A mapping is established to that of a quantum particle in a random potential, and the phenomenon of localization is explained in terms of the dominance of localized tail states of the Schrödinger equation. We also give a physical interpretation of the 1-step replica-symmetry-breaking solution, and elucidate the connection with the statistics of localized tail states. We proceeded to discuss the more realistic case of a chain embedded in a sea of hard obstacles. Here, we show that the chain size exhibits a rich scaling behavior, which depends critically on the volume of the system. In particular, we show that a medium of hard obstacles can be approximated as a Gaussian random potential only for small system sizes. For larger sizes a completely different scaling behavior emerges. Finally we consider the case of a polymer with self-avoiding (excluded volume) interactions. In this case it is found that when disorder is present, the polymer attains a conformation consisting of blobs connected by straight segments. Using Flory type free energy arguments we analyze the statistics of these conformational shapes, and show the existence of a localization-delocalization transition as a function of the strength of the self-avoiding interaction. | |
| dc.description | To be published as a book chapter in "Statistics of Linear Polymers in Disordered Media", edited by B.K. Chakrabarti, Elsevier 2005 | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0411195 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0411195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/25228 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Statistical Mechanics | |
| dc.title | Localization of Polymers in Random Media: Analogy with Quantum Particles in Disorder | |
| dc.type | text |