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Doctoral Thesis
DOI
https://doi.org/10.11606/T.43.2000.tde-02122013-184622
Document
Author
Full name
Léa Ferreira dos Santos
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Committee
Escobar, Carlos Ourivio (President)
Mizrahi, Salomon Sylvain
Moussa, Miled Hassan Youssef
Pleitez, Vicente
Wreszinski, Walter Felipe
Title in Portuguese
Aspectos dos Fundamentos da Mecânica Quântica: Processos Estocásticos e Analogia com Turbulência
Keywords in Portuguese
Física teórica
Mecânica quântica
Processos estocásticos
Turbulência
Abstract in Portuguese
Nesta tese apresentamos algumas possíveis interpretações para a descrição dos fenômenos quânticos. Fazemos uso da interpretação estocástica de Nelson para descrever uma corda bosônica aberta e mostramos que os resultados coincidem com aqueles obtidos via primeira quantização. Combinamos ainda esta interpretação, que lida com a posição da partícula, com um particular modelo de localização da função de onda conhecido como CSL, o que nos permite analisar a influência da evolução da função de onda sobre o movimento da partícula. A função de onda desses modelos de redução realiza um movimento estocástico no espaço de Hilbert devido à adição de um ruído multiplicativo na equação de Schrödinger. Mostramos que a partícula, por sua vez, sofre movimento turbulento, o que motiva uma analogia entre sistemas quânticos abertos e turbulência, de forma semelhante à que já havia sido realizada entre sistemas quânticos isolados e movimento browniano.
Title in English
Aspects of the foundations of quantum mechanics: stochastic processes and analogy with turbulence.
Keywords in English
Quantum mechanics
Stochastic processes
Theoretical physics
Turbulence
Abstract in English
In this thesis we present some possible interpretations for the description of quantum phenomena. We make use of Nelson's stochastic interpretation to describe an open bosonic string and show that the results coincide with those obtained from the first quantization. Moreover, we combine this interpretation, which deals with the particle position, with a particular localization model for the wave function known as CSL, which allows us to analyse the influence of the wave function evolution on the movement of the particle. The wave function af these reduction models performs a stochastic motion in Hilbert space due to the addition of a multiplicative noise in the Schrödinger equation. We show that the particle, on the other hand, suffers a turbulent motion, which motivates an analogy between open quantum systems and turbulence, similarly to what had already been done between isolated quantum systems and brownian motion.
 
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Publishing Date
2014-02-21
 
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