Semiclassical approximation with zero velocity trajectories

Semiclassical Propagation of Wavepackets with Complex Trajectories

We derive a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also consider additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller’s thawed gaussian approximation. The other appro...

Semiclassical Nonadiabatic Dynamics with Quantum Trajectories

Unstable semiclassical trajectories in tunneling.

Some tunneling phenomena are described, in the semiclassical approximation, by unstable complex trajectories. We develop a systematic procedure to stabilize the trajectories and to calculate the tunneling probability, including both the suppression exponent and prefactor. We find that the instability of tunneling solutions modifies the power-law dependence of the prefactor on Planck's variant a...

Semiclassical Dynamics with Quantum Trajectories: Formulation and Comparison with the Semiclassical Initial Value Representation Propagator

Fermion Tunneling Beyond Semiclassical Approximation

Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in [11] for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking tempe...