Measurements of the absorption spectrum of atomic H in strong magnetic fields have been analyzed. The measurements, performed by the Bielefeld, Germany experimental group, investigated the photoabsorption to levels near the ionization threshold in magnetic fields ranging from 2.7 to 6 Tesla. Taking advantage of a classical scaling law, the photon energy and the magnetic field strength were varied simultaneously in the experiment and the absorption rate vs. B{dollar}\sp{lcub}-1/3{rcub}{dollar} at fixed scaled-energy, {dollar}\varepsilon{dollar} = E/(B/B{dollar}\sb{lcub}\rm o{rcub})\sp{lcub}2/3{rcub}{dollar} was measured. The absorption rate was observed to exhibit sinusoidal fluctuations which we correlate with closed classical orbit of the electron. A Fourier transformation of this signal yields peaks which we interpret as "recurrence strengths" which depend upon the classical action of the closed orbit. Closed-orbit theory gives formulas for these recurrence strengths. as the scaled energy is increased, observed recurrences proliferate, consistent with the change from orderly to chaotic motion of the electron. Bifurcation theory provides organizing principles for understanding this proliferation and for interpreting the data. New "exotic" orbits suddenly appear "out of nowhere" through saddle-node bifurcations. The "main sequence" of orbits is produced from an orbit parallel to B through a sequence of pitchfork and period-doubling bifurcations. Other recurrences are created by period-tripling and higher-order bifurcations of existing orbits. These bifurcations can have generic structure, or sometimes the structures are modified by symmetries of the system. Focusing effects associated with these bifurcations cause some recurrences to be particularly strong.
| Identifer | oai:union.ndltd.org:wm.edu/oai:scholarworks.wm.edu:etd-3747 |
| Date | 01 January 1993 |
| Creators | Shaw, John A. |
| Publisher | W&M ScholarWorks |
| Source Sets | William and Mary |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations, Theses, and Masters Projects |
| Rights | © The Author |
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