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Master's Dissertation
DOI
https://doi.org/10.11606/D.76.2009.tde-10032009-100817
Document
Author
Full name
Felipe Lorenzen
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2009
Supervisor
Committee
Moussa, Miled Hassan Youssef (President)
Almeida, Norton Gomes de
Fontanari, Jose Fernando
Title in Portuguese
Extensão dos Be-ables de Bell e Competição Atenuação x Amplificação
Keywords in Portuguese
Be-ables. Sistemas Quânticos Abertos. Equações Mestras. Equação estocástica de Itô.
Abstract in Portuguese
Na primeira parte deste trabalho empregamos a equação estocástica de Itô para obter uma interpretação generazilada de be-ables, que engloba dissipação, decoerência e a transição da dinâmica quântica para clássica. Ao escolher uma fonte de estocasticidade que leva à correção dissipativa da dinâmica hamiltoniana na forma de Lindblad, obtemos uma nova classe de trajetórias que incorpora às trajetórias de Bohm o termo difusivo presente na formulação de Nelson. Utilizando nossa formulação extendida dos be-ables identificamos o processo de decoerência e verificamos que este encontra-se em concordância com o formalismo quântico usual. Na segunda parte deste trabalho analisamos a dinâmica de um sistema quântico sob a competição de dois sistemas multimodais contra-atuantes: um atenuador ou reservatório térmico e um amplificador de Glauber. Mapeamos o comportamento dinâmico deste sistema, identificando diferentes regimes de parâmetros. Calculamos o processo de decoerência emergente da ação dos sistemas multimodais e discutimos aplicações para o nosso sistema. Na terceira parte deste trabalho, usamos a abordagem de campo médio para a obtençãoo da equação mestra que descreve o problema da superradiância sob a ação de flutuações térmicas do reservatório. Desejamos com isso explorar a possibilidade de se verificar o processo de ressonância estocástica no âmbito da superradiância.
Title in English
Extended Bell´s Be-ables and Atenuattion × Amplification Competition.
Keywords in English
Be-ables. Open quantum systems. Master equation. Itô stochastic equation.
Abstract in English
In the first part of this work we employ the Itô stochastic equation to extend Bells be-able interpretation of quantum mechanics to encompass dissipation, decoherence and quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad type correction to the Hamiltonian dynamics, we verify that the diffusive term in Nelson´s formalism is naturally incorporated into Bohm´s one, rendering a unified Bohm-Nelson theory. Mainly, analyzing the intereference between quantum trajectories, we clearly identify the decoherence time, as estimated from the usual quantum formalism. We also observe the quantum-to-classical transition through the convergence of the infinite possible quantum trajectories to their associated classical counterparts. In the second part of this work we analyze the dynamical behavior of a quantum system under the actions of two counteracting baths: the inevitable energy draining reservoir and, oppositly, an enginereed Glauber amplifier feeding the system excitation. We trace the system dynamics towards equilibrium to mapp its distinct behaviors following from the attenuation × amplification interplay. The decoherence process emerging from the action of both counteracting baths is also computed and, finally, applications of such an attenuation × amplification competition is discussed. Finally, in the third part of this work we employ the mean field approximation to derive the master equation describing the process of superradiant emission under the presence of thermal fluctuation. We envisage to explore the possibility of observe stochastic resonance within the superradiant process.
 
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Publishing Date
2009-03-24
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • Lorenzen, F., et al. Quantum system under the actions of two counteracting baths: A model for the attenuation-amplification interplay [doi:10.1103/PhysRevA.80.062103]. Physical Review. A [online], 2009, vol. 80, p. 062103.
  • Lorenzen, F., de Ponte, M., and Moussa, M. Extending Bell s beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories [doi:10.1103/PhysRevA.80.032101]. Physical Review. A [online], 2009, vol. 80, p. 032101.
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