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| Chaos Theory and Nonlinear Dynamics | |
In the latter 1950s, the late Georgia Tech physicist Joseph
Ford began investigating the scientific phenomena of chaos,
described by him as "deterministic randomness." Ford, the self-
avowed "Evangelist of Chaos," was a pioneer in this relatively
new field of science. During his decades of research in the area,
he moved from an evolutionary to a revolutionary view of chaos,
ultimately declaring it the key to the future of all science.
In the 1960s, Ford conducted computer experiments that
verified and extended the results of work in chaos published in
the 1950s. Ford said he demonstrated that many systems exhibited
such completely unexpected, wildly erratic behavior that
intuition suggested scientists were observing the
long-anticipated deterministic randomness in Newtonian dynamics. There
was little argument against his assertions.
By the late 1970s, Ford and an Italian colleague had unified
disciplines ranging from astronomy to zoology in their findings
related to chaos. They started a new journal of nonlinear science
called Physica D.
Later in the decade, Ford embraced a Soviet
colleague's new algorithmic complexity theory, which provides
both qualitative and quantitative measures of nature's
complexity. From this time on, Ford referred to a revolutionary
view of chaos and encountered many arguments against his
theories. He believed the theory of chaos indicates the universe
is completely random.
In the 1980s, Ford and Georgia Tech physicist Ronald Fox
worked individually to define chaos at the quantum mechanical
level and to use those definitions to determine if quantum
systems exhibit chaos. At that time, no quantum models had
exhibited true chaos over the long term, like their classical
model counterparts did. Ford showed the quantum description of
chaos is actually only quasiperiodic. On the basis of algorithmic
complexity theory, he believed errors existed in the foundations
of quantum mechanical theory, and that quantum models could not
exhibit chaos.
Fox, on the other hand, believed quantum mechanics
would yield a quantum signature of classical chaos that
paralleled the classical definition. By the mid-1990s, Fox had
approached the chaos and quantum-classical correspondence
problems from a general perspective, rather than from the
behavior of any particular model system.
His studies showed
strong quantitative correspondence between the evolution of
initial sharply localized wave packets and evolution of
associated classical ensembles. By measuring the initial growth
rate of the quantum variances, the local classical Lyapunov
exponent (the universal hallmark of classical chaos) could be
determined. Fox concluded that quantum-classical correspondence
for chaotic dynamics does not require notions involving infinite
time and that the local Lyapunov exponent
is a quantum signature of classical chaos.
Following on Ford and Fox's groundbreaking work in chaos, Dr.
Rajarshi Roy, former chair of the
School of Physics, and his
colleagues learned to control the chaotic fluctuations in light
intensity produced by certain laser systems. In 1994, Roy and Dr.
K. Scott Thornburg of Georgia Tech showed for the first time that
two chaotic lasers could be synchronized. At that time, they
suggested potential communications-related applications for the
work.
Subsequently, Roy and Dr. Quinton Williams, a former
Georgia Tech Ph.D. student, studied erbium-doped fiber lasers and
amplifiers with the goal of using them for chaotic
communications. Then in 1998, Roy and Georgia Tech graduate
student Gregory Van Wiggeren used chaotic fluctuations in light
intensity to encode information being transmitted from one laser
to another through fiber optic cable. This research opens the
possibility of using chaotic carrier signals to hide "private"
messages transmitted across existing optical fiber networks.
Georgia Tech file photo
In 1994, Georgia Tech researchers, including Dr. Scott
Thornburg (above), showed for the first time that two chaotic
lasers could be synchronized. He and Dr. Rajarshi Roy, former
chair of the School of Physics,
suggested potential
communications-related applications for the work.
For more information, contact Dr. Ronald Fox, School of Physics, Georgia
Tech, Atlanta, GA 30332-0430. (Telephone: 404-894-5260) (E-mail:
ronald.fox@physics.gatech.edu)
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