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Tesi etd-07052009-145916


Thesis type
Tesi di laurea specialistica
Author
DE LUCA, GIANCARLO
URN
etd-07052009-145916
Title
Linear response theory for complex systems
Struttura
SCIENZE MATEMATICHE, FISICHE E NATURALI
Corso di studi
SCIENZE FISICHE
Commissione
relatore Grigolini, Paolo
Parole chiave
  • complex systems
  • liquid crystals
  • linear response
Data inizio appello
21/07/2009;
Consultabilità
completa
Riassunto analitico
We present in this work a proposal for modeling perturbation on complex systems.
Kubo's Theorem can be derived only for systems whose correlation function is stationary. When the correlation function becomes non - stationary Kubo's linear response function can be extended in two different ways. We show - first for dichotomous systems then for general ones - that this corresponds in assuming that the perturbation acts either on the event generating operator (thus perturbing the leading process without affecting the event occurrence time) or on the global interaction (then perturbing our waiting time distribution). We call the first approach "phenomenological" and the second one "dynamical".
We assert that the “dynamical” approach is the one, which better describes our processes and then extend this theory to non dichotomous processes. In this case, besides the linear response term, a new term appears. We then show that for a harmonic perturbation the response is a dumped harmonic perturbation with amplitude a phase depending on depending on the peculiar characteristics of the system .
We then illustrate an experimental result on Liquid crystals dynamics that confirms our theory.
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