Chaos and low-order corrections to classical mechanics or geometrical optics.

Abstract

Based on simple first-order quantum corrections to classical equations of motion, which we show to be closely related to Gaussian wave-packet dynamics (GWD) and a time-dependent variational principle (TDVP), we deduce that quantum corrections to classical dynamics should typically become most pronounced when the classical system becomes chaotic. The time duration over which classical dynamics, GWD, or TDVP may provide good approximations is much shorter when the classical dynamics are chaotic. However, for certain situations involving very short laser pulses, these approximations can be very accurate. The same concepts are applicable to paraxial wave optics, which may offer simpler experimental studies of ``quantum chaos'': the distinction between classical and ``quantum'' chaos is in large part the distinction between ray versus wave behavior.