Semiclassics around a phase space caustic: an illustration using the Nelson Hamiltonian
arXiv:1009.2080 · doi:10.1016/j.physleta.2010.12.051
Abstract
The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the calculation. Eventually, however, two contributing trajectories coalesce, characterizing what is called phase space caustic. In this case, the usual semiclassical formula for the propagator diverges, so that a uniform approximation is required to avoid this singularity. In this paper, we present a non-trivial application illustrating this scenario, and showing the accuracy of the uniform formula that we have previously derived.
6 pages, 2 figures
References in corpus (4)
- Semiclassical theory of spin-orbit interaction in the extended phase space
- A Uniform Approximation for the Coherent State Propagator using a Conjugate Application of the Bargmann Representation
- Controlling Phase Space Caustics in the Semiclassical Coherent State Propagator
- A conjugate for the Bargmann representation