Long-time and unitary properties of semiclassical initial value representations.
We numerically compare the semiclassical "frozen Gaussian" Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the "thawed Gaussian" propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear one-dimensional potentials. The reasons for the lack of long-time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy.
Harabati
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Max-Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, D-01187 Dresden, Germany. harabati@mpipks-dresden.mpg.de
Rost
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Grossmann
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