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R E S E A R C H
I N T E R E S T S
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Short term:
- Frequency-dependent linear response theory in low-dimensional
conductors at finite damping, and semiclassical evaluation of the resulting
expressions.
- Evidence of the KAM transition
and classical phase space transport in wave calculations
- Classical dynamics in ``centrifugal billiards''
Two-dimensional euclidean billiards with an additional $1/r^2$
potential arise naturally in the study of deformed droplets (and
nuclei) with axial symmetry.
- Billiards with three degrees of freedom
A promising approach to the little-studied case of truly
three-dimensional billiards would be to consider them as deformations
of some body of revolution like the centrifugal billiard or a
truncated cylinder. Complications like Arnold diffusion and non-KAM
behavior can thus be controlled. We are studying cylinders with tilted
caps.
- Interplay between mode-specific Q-spoiling, spatial
hole burning, and gain saturation in ARC
The experimental agreement with our predictions for lasing
directionality in deformed droplets has not yet been tested at a fully
quantitative level. This is due in large part
to the intricate multimode lasing scenario which arises
because of spatial hole burning, and which must be taken into account
in determining the weighting of different lasing
modes.
- Novel experimental realizations of ARC devices
Microdroplets in aerosols have proved to be well suited for initial
tests of our predictions. Similar physics applies to glass spheres and
microdisc lasers where it is currently of great interest to manipulate
the cavity shape so as to couple light out in a highly
directional manner, as opposed to the inefficient
isotropic emission pattern from perfectly symmetric devices. Design of
such cavities can be guided by an understanding of the nonlinear ray
dynamics.
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