A new mixed quantum/semiclassical propagation methodology

Neepa T. Maitra, Eric J. Heller

Jiushu Shao

Abstract A simplified formulation of the semiclassical Heisenberg operator based on the forward‐backward evolution methodology is worked out. A new representation related to the Husimi form is suggested to remove its problem, which may also offer a new way to improve the Herman‐Kluk semiclassical propagator.

F. Nicacio, Alfredo Ozorio de Almeida, K. Dechoum +1 more

Guangcan Yang

In this paper a semiclassical propagator in a mixed position–momentum space is derived in the formalism of Maslov's multi-dimensional semiclassical theory. The corresponding mixed van Vleck determinant is also given explicitly. The propagator can be used to locally fix semiclassical divergences in singular regions of configuration space. It is shown that when a semiclassical propagator is transformed from one representation to another, its form is invariant.

Robert Hammerling, J. Kamleitner, Othmar Koch

Radka Bach, Keith R. Burnett, M. B. d’Arcy +1 more

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wave packets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wave-function dynamics.