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Master's Dissertation
DOI
10.11606/D.3.2016.tde-25072016-143517
Document
Author
Full name
Ulisses Alves Maciel Neto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Silva, Paulo Sergio Pereira da (President)
Piqueira, José Roberto Castilho
Ragazzo, Clodoaldo Grotta
Title in Portuguese
Rastreamento adiabático de ensembles quânticos via medianização.
Keywords in Portuguese
Controle (Teoria de sistemas e controle)
Equações de Bloch
Mecânica quântica
Medianização
Ressonância nuclear magnética
Sistemas dinâmicos
Abstract in Portuguese
Este trabalho aborda o problema da inversão do vetor momento magnético, com ampla aplicação na Ressonância Nuclear Magnética (RNM). Em vez de uma sequência de impulsos e de abordarmos somente o problema de conduzir o vetor de -e3 para +e3, escolhemos uma lei de controle limitada e analisamos o processo de várias iterações (voltas completas). Através do método da medianização, obtemos uma solução explícita aproximada para o sistema e, através dela e de alguns teoremas auxiliares sobre rotações, discutimos a propagação do erro em módulo e fase cometido após a realização dessas iterações.
Title in English
Adiabatic following of quantum ensembles using averaging.
Keywords in English
Averaging
Bloch equations
Nuclear magnetic resonance
Quantum control
Abstract in English
This dissertation considers the problem of inversion of the magnetic moment vector, with wide application in Nuclear Magnetic Resonance (NMR). Instead of a pulse sequence and only approach the problem of driving the vector from -e3 to +e3, we choose limited controls and we analyze several iterations of the process (laps). By the averaging method, we obtain an approximate explicit solution for the system and through this method, together with some auxiliary theorems on rotations, we discuss the propagation of error in magnitude and phase committed after performing these iterations.
 
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Publishing Date
2016-07-25
 
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