Quantum and classical dynamics in the stadium billiard

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Abstract
Classical and quantum dynamics in the classically chaotic stadium billiard are compared through studies of the evolving phase-space distributions and expectation values. Good agreement between the two mechanics is found for all distributions other than vertically directed wave packets which contain significant contributions from pseudoregular quantum eigenstates. Despite formal arguments as to the absence ‘‘quantum chaos’’ the quantum dynamics clearly shows a time-averaged relaxation to equilibrium, over the timescale studied, which is consistent with the classical K-system behavior.