Report for the academic year - Libraries - Institute for Advanced Study

SCHOOL •
STEPHEN L. ADLER, Particle Physics, New Jersey Albert Einstein Professor
)OHN N. BAHCALL, Astrophysics, Richard Black Professor
P1ET HUT, Astrophysics
NATHAN SEIBERG, Theoretical Physics
FRANK WILCZEK, Theoretical Physics, J. Robert Oppenheimer Professor
EDWARD W1TTEN, Mathematical Physics, Charles Simonyi Professor
PAWAN KUMAR, Astrophysics
FREEMAN J. DYSON, Mathematical Physics and Astrophysics
PROFESSOR STEPHEN ADLER'S time this year was divided between work on modi-
fied forms of quantum mechanics, in particular phenomenological modifications of the
Schrodinger equation, and work on particle phenomenology.
In the area of quantum mechanics, Adler expanded a manuscript co-authored with
Horwitz into a paper giving a detailed study of the structure and properties of the
Hughston stochastic Schrodinger equation, including an analysis of its relation to other
proposed stochastic equations and an initial discussion of empirical issues. One signifi-
cant added result is that only when the dissipation is driven by an operator commuting
with the Hamiltonian does one get a stationary limiting behavior at all; as shown in the
paper, in this case the limiting probabilities for various final states to occur agree with the
quantum mechanical probabilities computed from the initial state. The use of Ito calcu-
lus methods in this paper led Adler to a new, and very simple, understanding of the Lind-
blad structure for the generator of a completely positive density matrix evolution, as an
infinitesimal Ito specialization of the Kraus form for a global, completely positive densi-
ty matrix map. As part of a continuing phenomenological study, in collaboration with
graduate student Indrajit Mitra, of whether the Hughston equation can give a satisfacto-
ry empirical account of state vector collapse, Adler found an exact solution of a simple
model for the statistical fluctuations in the number of adsorbed model on an active
surface. (The mass fluctuations associated with such molecules play a crucial role in the
Hughston equation model for state vector reduction.) He also gave a review talk on the
role of probability in quantum mechanics, focusing on the issue of postulated
versus emergent probabilities, at the Ischia conference on Chance in Physics in late
November. Additionally, Professor Adler gave an unpublished survey talk, "Explorations
in Quantum Mechanics," reviewing highlights of his work on quantum mechanics, at the
conference Symmetry Found and Lost held at the Institute in mid-October in honor ot his
60 th birthday.
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