Quantum corrections 1 / N the classical limit: Application to the Lipkin model SU(2)

Author(s)

Marcelo Trindade dos Santos

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 1997-07-17

Examining board members

Maria Carolina Nemes; Marcus Aloizio Martinez de Aguiar; Alfredo Miguel Ozorio de Almeida; Caio Henrique Lewenkopf; Celso Luiz Lima

• Advisor: Maria Carolina Nemes

Abstract

We show how the time dependent variational principle can be used to study quantum corrections to the classical limit, in particular of the SU(2) Lipkin Model. We show how much corrections can be cast in Hamiltonian form, coupling to the classical dynamics a set of variables associated to the quantum fluctuations. This leads to an effective dynamics which has the number of degrees of freedom doubled with respect to the classical system. As a consequence chaotic behavior emerges. We show that this semiquantal chaos is the mechanism through which tunneling is effected, and also, that these corrections systematically improve the classical results and propose some quantitative measure of this improvement. (AU)