"Einstein's unknown insight and the problem of quantizing chaotic
motion"
Douglas
Stone
Yale University
Department of Applied Physics
Abstract: In 1917 Einstein authored a little-known paper
on the problem of generalizing the old quantum theory to problems
with several degrees of freedom that are not separable. This
paper was his only published work on the correct quantization rule for
matter, which was of course not known at that time. His work laid
the foundation for a method which is completely correct (within its
sphere of applicability), now known as Einstein-Brillouin-Keller
quantization, a multi-dimensional generalization of the WKB
approximation. However he pointed out that the method fails
if there do not exist a number of integrals of motion equal to
the number of degrees of freedom, i.e. unless the system is
integrable. He suggested that non-integrable classical dynamics
is typical and presents an open problem for quantum theory.
This brilliant insight was ignored until the late sixties when it
became well-known to physicists that partially chaotic motion is indeed
generic in classical mechanical systems. The problem
noted by Einstein is fundamental and has never been fully
overcome; but alternative semiclassical approaches to the quantum
mechanics of classically chaotic systems have been developed and
applied to interesting problems in atomic, condensed matter and optical
physics.
I will review Einstein's arguments and place them in a
modern context. Then I will mention a few experimental
systems to which "quantum chaos theory"can be applied, focusing
on the topic of chaotic dielectric microlasers studied at Yale and
elsewhere
Time: 3:00 pm
Location: Lecture Room 3
The reception
will be at 2:00~3:00 pm in room N201