Semiclassical propagation of coherent states

Author(s)

Fernando Roberto de Luna Parisio Filho

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2005-03-29

Examining board members

Marcus Aloizio Martinez de Aguiar; Alfredo Miguel Ozório de Almeida; Caio Henrique Lewenkopf; Kyoko Furuya; Amir Ordacgi Caldeira

• Advisor: Marcus Aloizio Martinez de Aguiar
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Indexed in: Base Acervus-UNICAMP; Biblioteca Digital da UNICAMP
• Location: Universidade Estadual de Campinas (UNICAMP). Biblioteca Central; T/UNICAMP; P219p; Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin; T/UNICAMP; P219p

Abstract

This thesis addresses di®erent aspects of the semiclassical propagation of coherent states. We have derived a general expression for the propagator connecting these states which, di®erently from previous formulae in the literature, is valid for packets of arbitrary widths. The result, obtained via functional integration, depends on classical trajectories in a complex phase space. Approximations based on real orbits are also analyzed and it is demonstrated that the Heller and BAKKS Gaussian propagators belong to the same category. Next we make a detailed study of the semiclassical propagation of coherent states in the position representation. The obtained formal results are applied to the case of a Gaussian packet under the influence of a smooth repulsive potential. For this system the solution of Hamilton's equations and the semiclassical wave function can be expressed analytically. The problem of non-contributing solutions, which originates from the application of the stationary exponent method, is solved by the introduction of some criteria of physical consistency. The e®ects of caustics in phase space, points where the lowest order semiclassical approximation diverges, are controlled by introducing corrections involving Airy functions (AU)