# Nonlinear Dynamics

Nonlinear dynamics is the study of systems that are described by nonlinear equations of motion. Chaos is a topic of particular interest. This topic is important in almost every branch of science and engineering. Our faculty study chaos two ways: as a phenomenon of classical mechanics, and as quantum chaos, which is the study of the interface between the quantum and classical descriptions for classically chaotic systems. The department offers a second semester of classical mechanics devoted to nonlinear dynamics.

Our inter-disciplinary research in nonlinear dynamics allows students to choose an experimental or theoretical project. Students can choose a theoretical project and apply the methods of chaos to field theory or to the many body problem. Additionally, students may choose an experimental project, studying the observable effects of chaos in plasmas, where the exchange of energy amongst waves and particles is chaotic. Our previous work on chaos has been published in leading journals such as *Physical Review Letters* and reported as invited talks at major conferences. One of our previous PhD students received a major national prize for a thesis on nonlinear dynamics.

*Theoretical elementary particle physics; lattice gauge theory; optical lattices.*

- Lattice field theory
- Renormalization group methods
- Composite Brout-Englert-Higgs bosons
- Decays of B-mesons (with the theory group at Fermilab)
- Gauge interactions on optical lattices
- Numerical simulations on home made clusters and at national facilities
- Quantum Field Theory methods: Feynman diagrams, strong-coupling expansion, large-N approximations
- Employment of former students: postdocs at five major universities in the U.S. and one in Ireland; senior research scientist in driving simulation project; software engineer in industry; college instructor; medical physics
- Students can be involved with the theory group at Fermilab
- Students are involved weekly in two seminars
- Students travel to summer schools and conferences

*Theoretical nuclear physics; mathematical physics.*

- Current Research: Supported by NSF and DOE Office of Science
- Relativistic few-quark and few-nucleon models of light nuclei and nucleons
- Leptonic probes of few hadron systems
- Scattering using Minkowski path integrals
- Multi-scale wavelet representations of quantum fields
- The vacuum in quantum field theory
- Euclidean formulations of relativistic quantum mechanics and quantum field theory
- Numerical methods based on wavelets

*Laser spectroscopy; plasma physics.*

- Experimental topics include experiments for plasma waves and instabilities, plasma self-organization and sheaths, and laser-induced fluorescence and wave-absorption diagnostics of plasmas
- Student projects are typically experimental with a significant interaction with theory
- Theoretical topics include plasma kinetic theory including waves and nonlinear fluctuations
- There are two labs at Iowa, including: a 3-meter linear magnetized-plasma device and a large multi-dipole discharge. Both are equipped with single-frequency scanning lasers for high-resolution laser spectroscopy. Some students also participate in collaborations on the Large Plasma Device located at UCLA
- Beyond interactions with group members, students participate in the plasma seminar and interact with Departmental theoretical and experimental plasma, space physics, and astronomy faculty
- Students develop skills including data analysis, high-resolution laser spectroscopy, designing and building apparatus, electronics, computation
- Previous assistants have found employment in academia, national laboratories, and in industry