Report for the Academic Year 1992-1993 - The Institute Libraries ...

THE SCHOOL OF NATURAL SCIENCES
in "Communications in Mathematical Physics." Others have resulted in preprints
and papers by Bleher alone. The general aim of this work is to understand the
effects of the transition from order to chaos in a classical dynamical system upon
the statistical behavior of eigenstates in the corresponding quantum system. They
are looking in detail at the eigenvalue statistics of classical systems that are com-
pletely integrable and so have maximal order. Numerical evidence suggests that
classical order goes with quantum disorder and vice versa. But no rigorous
statement of the inverse relationship between classical and quantum order has
been formulated, let alone proved. Dyson and Bleher hope that their work will
be a small step in this direction. They have had a lot of help from Peter Sarnak
in the Princeton University mathematics department.
Professor Dyson spent part of the year preparing lectures for delivery at a variety
of formal occasions. One was a Compton Memorial Lecture given at Washington
University in St. Louis in conjunction with a meeting of astronomers to discuss
the scientific output of the Compton Gamma-Ray Observatory now in orbit.
This lecture, with the title "Revolutions in Astronomy," was also given as a
Faculty Lecture to the Institute community. Another lecture, with the title "Sci-
ence and Ethics," was given at the Mellon Seminar on Science and Society at the
Institute. A third lecture, with the title "Homage to George Green," was given
in England in July 1993 at the celebration of George Green's 200th birthday. He
also gave convocation addresses at a couple of Hberal arts colleges under the title
"The Scientist as Rebel."
PIET hut's research has focused on the study of dense stellar systems, with
applications to globular star clusters and galactic nuclei. He has taken part in the
design of large-scale simulations in coUisional stellar dynamics, to be performed
on the 1 Tflops special-purpose computer under development in the astronomy
department at Tokyo University. As part of this effort, new tree-based algo-
rithms for the treatment of close encounters and physical collisions were devel-
oped in collaboration with Jun Makino from Tokyo University and Steve
McMillan from Drexel University.
Other studies of globular clusters included a series of Fokker-Planck simulations
of post-collapse evolution, in which a detailed investigation was made of the
properties of gravothermal oscillations, in collaboration with Joseph Breeden
and Haldan Cohn of Indiana University. A theoretical study of the formation
and dynamical evolution of stellar-mass black hole remnants in globular clusters
was carried out in collaboration with Shri Kulkarni from the California Institute
of Technology and Steve McMillan. This work resulted in potentially interesting
observational consequences, by predicting a significant formation rate of black
hole containing X-ray binaries.
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