Abstract
We study the semiclassical propagation of squeezed Gaußian states. We do so by considering the propagation theorem introduced by Combescure and Robert (1997 Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow Asymptot. Anal. 14 377–404) approximating the evolution generated by the Weyl-quantization of symbols H. We examine the particular case when the Hessian H″(Xt) evaluated at the corresponding solution Xt of Hamilton's equations of motion is periodic in time. Under this assumption, we show that the width of the wave packet can remain small up to the Ehrenfest time. We also determine conditions for ‘classical revivals’ in that case. More generally, we may define recurrences of the initial width. Some of these results include the case of unbounded classical motion. In the classically unstable case we recover an exponential spreading of the wave packet as in Combescure and Robert (1997 Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow Asymptot. Anal. 14 377–404).
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