2026-09-21T16:55:14Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/45467 2023-07-11 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Goldbart, Paul M. Stone, Michael Goldbart, Paul M. Abbamonte, Peter M. Weaver, Richard L. Rocklin, David Z. 2013-08-22T16:41:04Z 2013-08-22T16:41:04Z 2013-08 2013-08-22T16:41:04Z 2013-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-05-24T21:41:59Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Rocklin_David.pdf: 1544351 bytes, checksum: b0b6a18cbc7e6dbf527622f008a3303e (MD5) Made available in DSpace on 2013-08-22T16:41:04Z (GMT). No. of bitstreams: 2 David_Rocklin.pdf: 1544351 bytes, checksum: b0b6a18cbc7e6dbf527622f008a3303e (MD5) license.txt: 4063 bytes, checksum: 61e4324586193b47342e984a125cd7ea (MD5) http://hdl.handle.net/2142/45467 en Copyright 2013 David Z. Rocklin strongly interacting polymer fluids quantum-classical mapping Directed-polymer systems explored via their quantum analogs text Physics 1244 Physics 0240 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Physics -UIUC 10KS0240PHD