Chaos and the quantum-classical correspondence in the kicked pendulum

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Abstract
The problem of determining the quantum signature of a classically chaotic system is studied for the periodically kicked pendulum. In parallel with the observation that chaos creates exponential growth of intrinsic fluctuations in classical, macroscopic, dissipative systems, we find that the quantum variances initially grow exponentially if the corresponding classical description is chaotic. The rate of growth is connected to the corresponding classical Jacobi matrix and, thereby, to the largest classical Liapunov exponent. These connections are established by examining the correspondence between the quantum Husimi-O’Connell-Wigner distribution and the classical Liouville distribution for an ensemble. Explicit results for the kicked pendulum are presented.