CHAOS AND THE QUANTUM-CLASSICAL CORRESPONDENCE IN THE KICKED PENDULUM

The problem of determining the quantum signature of a classically chao tic system is studied for the periodically kicked pendulum. In paralle l with the observation that chaos creates exponential growth of intrin sic fluctuations in classical, macroscopic, dissipative systems, we fi nd that the quantum variances initially grow exponentially if the corr esponding classical description is chaotic. The rate of growth is conn ected to the corresponding classical Jacobi matrix and, thereby, to th e largest classical Liapunov exponent. These connections are establish ed by examining the correspondence between the quantum Husimi-O'Connel l-Wigner distribution and the classical Liouville distribution for an ensemble. Explicit results for the kicked pendulum are presented.