Coherent states: the symplectic goup and generalizations

Author(s)

Marcel Novaes

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2003-11-21

Examining board members

Jose Eduardo Martinho Hornos; Elcio Abdalla; Marcus Aloizio Martinez de Aguiar; Salomon Sylvain Mizrahi; Paulo Afonso Faria da Veiga

• Advisor: Jose Eduardo Martinho Hornos

Abstract

The subject of the Thesis was the aplication of the coherent states theory to non-trivial quantum systems. Starting from the general definition of coherent states for compact Lie groups, we made a detailed investigation of the construction of these states and its properties in the case of the unitary symplectic group Sp(4), which is extremely important in both quantum and classical mechanics. This group has an intermediate complexity, allowing an analytic treatment while presenting non-trivial properties from the point of view of represention theory of Lie algebras. The coherent states so obtained allowed us an investigation of the classical limit of systems with Sp(4) symmetry and a conection with the theory of chaos in quantum mechanics. Besides that, we have treated a recent generalization of the concept of coherent states for systems with discrete and nondegenerate spectrum, the Gazeau-Klauder states. These states were applied to a twodimensional magnetization problem and also to the onedimensional double-well potential, where we have observed the appearence of the so-called \"Schrödinger cats\", which consist in the superposition of two minimum-uncertainty states. (AU)