Wednesday, May 21

3:00 PM-5:00 PM Ballroom II - Level B

Applications of the Geometric Phase

This minisymposium will focus on recent and ongoing developments concerning the `geometric', or `Hannay-Berry' phase. The original setting in the pioneering paper by Berry (1984) was the adiabatic theorem from quantum mechanics dealing with a system coupled to a slowly changing environment. If the Hamiltonian varies adiabatically, then after a cyclic evolution of the environment parameters, the eigenstate returns to its original form, but with a geometric phase factor associated with it. Since this paper appeared, there has been a flood of ongoing work on both classical and quantum analogues of this phase factor and this minisymposium is meant to give a snapshot of current activity in this area.

Organizers: Jerrold E. Marsden, California Institute of Technology; and Paul K. Newton, University of Southern California

3:00 Geometric Phases and the Stabilization of Balance Systems
Jerrold E. Marsden, Organizer; Anthony Bloch, University of Michigan, Ann Arbor; Gloria Sanchez, University of Merida, Venezuela; and Naomi Leonard, Princeton University
3:30 The Phase for the Spatial Three-Body Problem
Richard Montgomery, University of California, Santa Cruz
4:00 Vortex Dynamics and the Geometric Phase
Paul K. Newton, Organizer
4:30 Coriolis Forces as an SO(3) Gauge Field: Applications to Molecular Dynamics
Robert G. Littlejohn, University of California, Berkeley

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TMP, 4/4/97