Elizabeth R. S. Burnim's research focuses on the intersection of condensed matter physics and advanced computational infrastructure, specifically modeling Andreev bound states in complex geometries. My work integrates theoretical physics with numerical solutions to resolve complex physical dynamics.
Current Investigations
- Matrix-Valued Riccati Transport Systems: I am developing matrix-valued Riccati transport formulations for quasiclassical nonequilibrium superconductivity. Moving beyond proof-of-concept, this project utilizes an integrated computational framework that resolves Andreev bound-state (ABS) spectra through a stabilized local density of states (LDOS) diagnostic.
- Coherence Dynamics in Interacting Systems: This research investigates the computational resolution of spectral singularities in nonlinear transport systems. Computational investigations explore simplified matrix-valued transport systems motivated by nonequilibrium superconductivity.
- Optical Field Perturbations: I am examining how coherence generates spatial structure in optical interference systems. Using fringe visibility, interference stability, and spatial pattern evolution, this work connects computational transport models with broader questions in photonics and wave dynamics.
Methodology & Technical Progress
The framework utilizes stabilized fixed-point propagation to solve the quasiclassical Eilenberger equations.
- Numerical Stability: Development of convergence protocols for non-commutative matrix transport in FEM frameworks.
- Topological Invariance: Characterization of the relationship between Riccati amplitude singularities and topological defects in confined fields.
- Analogue Gravity: Assessment of whether quasiclassical transport instabilities provide a computational model for nonlinear field dynamics in curved spacetime.