2007/08/28 by Eric Sträng
Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Hessian matrix #Laser-Matter Interactions and Applications #Mathematical physics #Mathematics #Network packet #Physics #Quantization (signal processing) #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Semiclassical physics #Wave packet #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/41/3/035307
arxiv created 2007/08/28 · openalex publication_date 2008/01/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 ''( X t ) evaluated at the corresponding solution X t 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).