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Doctoral Thesis
DOI
10.11606/T.43.1997.tde-15052012-141043
Document
Author
Full name
Marcelo Trindade dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1997
Supervisor
Committee
Nemes, Maria Carolina (President)
Aguiar, Marcus Aloizio Martinez de
Almeida, Alfredo Miguel Ozorio de
Lewenkopf, Caio Henrique
Lima, Celso Luiz
Title in Portuguese
Correções Quânticas 1/N ao Limite Clássico: Aplicação ao Modelo de Lipkin SU(2)
Keywords in Portuguese
Aproximação de campo médio
Caos
Limite semiclássico
Modelo de Lipkin
Tunelamento.
Abstract in Portuguese
Neste trabalho mostramos de que maneira o princípio variacional dependente do tempo pode ser usado para se estudar correções quânticas ao limite clássico, particularmente, no contexto do modelo de Lipkin SU(2). Mostramos que tais correções podem ser colocadas na forma Hamiltoniana, acoplando-se a dinâmica clássica um conjunto de variáveis associadas às flutuações quânticas, nos levando à uma dinâmica efetiva com o número de graus de liberdade dobrado em relação ao sistema clássico. Como conseqüência o comportamento caótico emerge. Mostramos que este caos semiquântico é o mecanismo através do qual o tunelamento se manifesta no espaço de fase. Mostramos que tais correções melhoram sistematicamente o resultado c1ássico, propondo um critério para quantificar esta melhora.
Title in English
Quantum corrections 1 / N the classical limit: Application to the Lipkin model SU(2)
Keywords in English
Chaos
Classical dynamics
Lipkin model
Abstract in English
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.  
 
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Publishing Date
2012-06-14
 
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