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Open Quantum Systems Decoherence

Controlling Phase Space Caustics in the Semiclassical Coherent State Propagator

arXiv

Authors: A. D. Ribeiro, M. A. M. de Aguiar

Year

2007

Paper ID

50531

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

The semiclassical formula for the quantum propagator in the coherent state representation <mathbf{z}" | e^{-ihat{H}T/hbar} | mathbf{z}'> is not free from the problem of caustics. These are singular points along the complex classical trajectories specified by mathbf{z}', mathbf{z}" and T where the usual quadratic approximation fails, leading to divergences in the semiclassical formula. In this paper we derive third order approximations for this propagator that remain finite in the vicinity of caustics. We use Maslov's method and the dual representation proposed in Phys. Rev. Lett. {\bf 95}, 050405 (2005) to derive uniform, regular and transitional semiclassical approximations for coherent state propagator in systems with two degrees of freedom.

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The semiclassical formula for the quantum propagator in the coherent state representation

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0704.2510 [2] arXiv https://arxiv.org/abs/0704.2510 [3] Publisher https://arxiv.org/abs/0704.2510

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