Caltech Student Receives Award for Simple Study of Complex Systems

PASADENA, Calif.— The trick to understanding a complex world, says Kathryn Todd, a graduate in '01 from the California Institute of Technology, is to study it from the bottom up.

Todd did just that with her senior thesis at Caltech, which looked at the subatomic world of electrons. For this work, Todd has been named the recipient of the 2002 LeRoy Apker Award from the American Physical Society (APS).

The Apker Award is intended to recognize outstanding achievements in physics by undergraduate students, and to thereby provide encouragement to young physicists who have demonstrated great potential for future scientific accomplishment. Each year, two undergraduates are presented the award. Todd, 22 and now a first-year graduate student at Stanford University, was chosen for her senior thesis, Studies of Double-Layer Two-Dimensional Electron Gases.

As an undergrad, Todd worked in the lab of James Eisenstein, a Caltech professor of physics, where she received her first exposure to conducting research from the bottom up. There she studied systems of about a million electrons that were contained in an area of less than a square millimeter.

"These systems are interesting," says Todd, "because even though physicists understand very well how one electron behaves, it's not so simple to understand what a million interacting electrons will do." Because electrons are charged, each electron is repelled from every other electron. It turns out, she notes, that just this simple interaction is enough "to make systems of electrons do beautiful and exotic things."

Such interactions between parts are responsible for the complexity of many systems in nature, Todd says, from enzymes in cells to entire ecosystems. "The difference between the systems we study and more complex systems," she says, "is that we are studying complexity in one of its simplest possible forms. Instead of taking the top-down approach of trying to understand the details of how one complex system works, we want to work from the bottom up to understand some of the universal features of complexity."

As part of her senior thesis, Todd wanted to learn something about the complex correlated state of electrons contained in less than a square millimeter of space. Specifically, she wanted to measure the "tunneling of electrons" from one thin layer to another through an energy barrier.

Electrons in such systems behave according to quantum mechanics, Todd notes. Quantum mechanics is based on the premise that energy and momentum are subdivided into small but measurable amounts. At subatomic levels, the effects of this phenomenon are significant. Entities normally thought of as particles, like electrons, can also behave like waves in certain situations, while entities normally thought of as waves, like light, can behave like particles. As waves, says Todd, electrons can slosh through energy barriers that they wouldn't be able to jump over as particles. That's tunneling. In the absence of a magnetic field, electrons are able to tunnel between the layers quite easily, but when the magnetic field is turned on, this tunneling is suppressed.

It turns out, says Todd, that this is because the magnetic field allows the electrons to avoid each other more efficiently than before. With a high magnetic field, they form a correllated state in each layer in which it is hard for an electron tunneling in from the other layer to find a space. But if the electrons in one of the layers are given enough energy to overcome this difficulty, tunneling turns on again. "By measuring the amount of tunneling versus the added energy," says Todd, "we hoped to learn more about the details of the correlated state. The data haven't yet led to a conclusive answer, but they've raised some very interesting possibilities."-