Elizabeth R. S. Burnim is an independent researcher in Bozeman, Montana, working on numerical methods for the quasiclassical theory of superconductivity and superfluid ³He. She is taking graduate coursework in physics at Montana State University, beginning fall 2026.
The work extends published scalar formulations of the Eilenberger–Riccati transport equations to matrix-valued coherence amplitudes, for confined geometries in which the order parameter has several components and surface states restructure the physics of the entire sample.
She came to this from aerospace engineering. The numerical machinery carries over more directly than the fields suggest: advection-dominated transport, characteristic sweeps, stabilization at gradient layers, and verification of a solver against something that is not itself.
Research
The current work is a finite-element solver for the Eilenberger–Riccati transport equations, self-consistent on the Matsubara axis and executed on GPU. It is verified against an exact analytic root and against an independent integrator sharing no code with it, rather than against a second discretization of the same program.
The target is confinement: films and slabs in which Andreev bound states formed at the surfaces reshape the free-energy landscape, and phases become stable that cannot exist in bulk.
Details are on the Research page.
The Silver Bridge
A retelling of this research through Greek mythology, written for young readers, to make superconductivity and its applications accessible to an audience that would not otherwise encounter them.
Painting
Some problems in this work are spatial before they are algebraic: how a field organizes itself across a region, where structure gives way, what a boundary does to the interior. Working those questions out on canvas is slower than working them out on paper, and slower is sometimes what is required. It is a way of holding a difficult idea long enough to see its shape.
The paintings are not illustrations of the physics and make no claim about it. They are where some of the thinking happens before it becomes precise.
Oil on linen. The current series is In Metamorfosi (2026).
Browse the Paintings gallery, or read about the current series, In Metamorfosi.
Contact
For academic inquiries, theoretical discussion, or collaboration: elizabeth@elizabethburnim.com