Nonlinear Dynamics of Electrons in Mesoscopic Semiconductor Nanostructures
D. K. Campbell,* G. P. Berman,* K. N. Alekseev, D. M. Pianto
NATO Linkage Grant, NANO.LG 931602

Quantum dots, quantum wires, and semiconductor heterojunction layers are of great interest for potential novel electronic devices. We studied the role of nonlinear dynamics in the transport of electrons through various mesoscopic nanostructures, including both vertical and lateral semiconductor superlattices and double-barrier resonance tunneling diodes focusing on effects created by the presence of external driving by both dc- and ac-electric and dc-magnetic fields. Our results include predicting (1) deterministic chaos in the electron current, which would appear experimentally as a substantial increase in the effective noise of the device and (2) symmetry-breaking (i.e., the development of a dc bias in response to a purely ac applied electric field or to a suitably aligned dc magnetic field). We are verifying these predictions through collaborations with several experimental groups.

Resonant and Transferal Interactions with Complex Systems
E. A. Jackson*
University of Illinois

Complex systems often have a large number of dynamic attractors with very different behaviors. The problem of obtaining a mathematical model that can describe the dynamics of such systems is a fundamental challenge in science. A new method of open-plus-closed-loop interactions on general systems of ordinary differential equations developed by Jackson and Grosu is being used experimentally to transfer systems among any of its attractors. It will also be used in a resonant-modeling technique to explore the most accurate global dynamic model of a system.

Search for Quantum Chaos
M. H. Nayfeh,* H. Thompson
University of Illinois

We are studying the question of the existence of chaotic behavior in quantum mechanical systems whose classical analogs are known to be nonintegrable and exhibit chaotic behavior. The system that we use is the interaction of low-frequency, high-power microwave radiation with one-dimensional hydrogen atoms. These atoms are prepared by laser excitation of atomic hydrogen in the presence of strong dc electric fields.