Boundary Effects in Critical Phenomena

Purdue University, West Lafayette IN

Investigators

Abstract

The goal of this research project is to advance the understanding of boundary effects and their underlying mathematical structures. The project deals with three models stemming from statistical physics. First, the two-species totally asymmetric exclusion process, is a discrete version of a system of two coupled Burgers equations. The PI proposes to determine a conjectured new sub-leading exponent of this system and to investigate the properties of the phase diagram in the presence of boundary terms. The second objective is the establishment of a correspondence between boundary terms in the boundary conformal loop model and the XX- and XXZ- quantum spin chains with boundary operators. The third subject is a Markov chain describing a growing and fluctuating interface in the presence of a wall. The PI will determine the critical exponent of boundary avalanches and investigate the connection to the discrete Boussinesq equation. The PI will employ methods ranging from Bethe-Ansatz to conformal field theory, finite-size scaling and Monte-Carlo simulations. The above projects will provide important insights into the theory of critical phenomena in the presence of boundary terms. The project is focused on three important areas, namely the role of boundaries in phase diagrams of statistical models, the classification of all boundary terms preserving conformal invariance in boundary conformal field theories and the influence of boundaries on Markov processes. There is also evidence that the outcome of the project will have implications for the theory of quantum computing. Broader Impact. The PI, holding a joint appointment in mathematics and physics, is fostering the interdisciplinary dialogue between these two departments by discussing research projects with colleagues in both departments. She is also supervising a graduate student working on a joint research project with the chemistry department. The project broadens the representation of women in the sciences with the PI actively serving as a role model for women in mathematics and physics, and her involvement in "Women in Science" and "Women in Physics" initiatives. She participates in science fairs through the the Science K-12 Outreach Program at Purdue University. She was invited by the mathematics department to teach an interdisciplinary course as a distance learning class.