Semiclassical propagation of coherent states using complex and real trajectories

Abstract

We study the semiclassical propagation of coherent states in $d$ dimensions, which in general involves complex classical dynamics. Several simple approximations are derived that depend only on real classical trajectories, among them the thawed Gaussian approximation (TGA). Apart from the TGA, all other possibilities are able to reproduce interference and tunnelling effects, and involve propagating a set of classical initial conditions compatible with the quantum uncertainties. The accuracy of the results is verified in two dimensions for the scattering by an attractive potential, for a bound nonlinear system, for motion inside a circular billiard and for a system involving tunnelling.

9 pages, 4 figures

References in corpus (2)

• Semiclassical Propagation of Wavepackets with Real and Complex Trajectories
• Mesoscopic Fluctuations of the Loschmidt Echo

Cited by in corpus (9)

• Interference in Bohmian Mechanics with Complex Action
• Complex trajectory method in time-dependent WKB
• Generalized Gaussian wave packet dynamics: Integrable and Chaotic Systems
• Path integral derivations of novel complex trajectory methods
• The semiclassical propagator in Fock space: dynamical echo and many-body interference
• Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators
• Semiclassical Tunneling of Wavepackets with Real Trajectories
• Evaluation of the semiclassical coherent state propagator in the presence of phase space caustics
• Semiclassical Ehrenfest Paths