Welcome to the Quantum
Chaos Home PageWelcome to the Quantum
Chaos Home PageMany systems in nature exhibit chaos (i.e. sensitive and exponential dependence on initial conditions), but their quantum analog do not. Interesting behaviour is seen in systems as one takes the semiclassical limit (h -> 0). For example, periodic orbits which are of measure zero in the classical systems are seen to be very important in organizing the quantum eigenvalues and eigenfunctions. It has also been found that systems which are classically chaotic, and those which are integrable belong to different Universality classes.
It has been shown that the statistics of eigenvalues, and eigenfunctions of classically chaotic sytems are similar to infinite symmetric matrices whose elements are random numbers. Futhermore, systems which have time reversal symmetry follow matries with real elements, and which do not have complex elements. Recently it has also been noted that the 0-dimensional sigma model of supersymmetry yields similar results to Random Matrix Theory.
In the past three decades, the field of `Quantum Chaos' has increasingly attracted more workers from Physics, Chemistry and Mathematics, as it has been seen to be manifested in Nuclear, Atomic and Molecular systems. More recently, Microwave cavity and Acoustic chaos experiments have also been done, and many features are found to be universal.
Last Updated 26 May 1995
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S. Sridhar