Directed-polymer systems explored via their quantum analogs

Rocklin, David Z.

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https://hdl.handle.net/2142/45467 Copy

Description

Title

Directed-polymer systems explored via their quantum analogs

Author(s)

Rocklin, David Z.

Issue Date

2013-08-22T16:41:04Z

Director of Research (if dissertation) or Advisor (if thesis)

Goldbart, Paul M.

Doctoral Committee Chair(s)

Stone, Michael

Committee Member(s)

• Goldbart, Paul M.
• Abbamonte, Peter M.
• Weaver, Richard L.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2013-08

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http://hdl.handle.net/2142/45467

Copyright and License Information

Copyright 2013 David Z. Rocklin

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