{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/45467"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/45467","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Directed-polymer systems explored via their quantum analogs","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Rocklin, David Z."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldbart, Paul M.","Stone, Michael","Abbamonte, Peter M.","Weaver, Richard L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-22T16:41:04Z","date_published":"2013-08-22T16:41:04Z","updated_at":"2026-07-22T22:25:36Z","subjects":["strongly interacting polymer fluids","quantum-classical mapping"],"languages":["en"],"rights":["Copyright 2013 David Z. Rocklin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/45467","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldbart, Paul M.","Stone, Michael","Abbamonte, Peter M.","Weaver, Richard L."]},{"key":"dc:creator","label":"Author","values":["Rocklin, David Z."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-08-22T16:41:04Z","2013-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["strongly interacting polymer fluids","quantum-classical mapping"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 David Z. Rocklin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/45467"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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)"]},{"key":"dc:title","label":"Title","values":["Directed-polymer systems explored via their quantum analogs"]}]}],"canonical_facts":{"dc:contributor":["Goldbart, Paul M.","Stone, Michael","Abbamonte, Peter M.","Weaver, Richard L."],"dc:creator":["Rocklin, David Z."],"dc:date":["2013-08-22T16:41:04Z","2013-08"],"dc:description":["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)"],"dc:identifier":["http://hdl.handle.net/2142/45467"],"dc:language":["en"],"dc:rights":["Copyright 2013 David Z. Rocklin"],"dc:subject":["strongly interacting polymer fluids","quantum-classical mapping"],"dc:title":["Directed-polymer systems explored via their quantum analogs"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:36Z"}