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Title:Directed-polymer systems explored via their quantum analogs
Author(s):Rocklin, David Z.
Director of Research:Goldbart, Paul M.
Doctoral Committee Chair(s):Stone, Michael
Doctoral Committee Member(s):Goldbart, Paul M.; Abbamonte, Peter M.; Weaver, Richard L.
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):strongly interacting polymer fluids
quantum-classical mapping
Abstract:The equilibrium statistical mechanics of classical directed polymers in D+1 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a quantum many-particle system in D spatial dimensions, with polymer con gurations corresponding to particle world-lines. This equivalence motivates the application of techniques originally designed for one-dimensional many-particle quantum systems to the exploration of many-polymer systems, as first recognized and exploited by P.-G. de Gennes [J. Chem. Phys. 48, 2257 (1968)]. In two dimensions, interactions give rise to an emergent polymer fluid, and I shall examine how topological constraints on this polymer fluid (e.g., due to uncrossable pins or barriers) and their geometry give rise to strong, entropy-driven forces. I shall also apply quantum techniques such as Bethe's Ansatz and bosonization to shed light on the structure of the polymer system. These techniques allow us to examine how polymer system correlations, thermodynamic properties, and response to impurities are influenced by strong polymer-polymer interactions. In three dimensions, polymers wind around one another and polymer topology may be incorporated via coupling to a Chern-Simons fi eld. As I discuss, this approach reveals the somewhat reduced role played by interactions in this higher-dimensional setting, leading to qualitatively diff erent polymer correlations, thermodynamic properties, and response to impurities.
Issue Date:2013-08-22
Rights Information:Copyright 2013 David Z. Rocklin
Date Available in IDEALS:2013-08-22
Date Deposited:2013-08

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