ETD

• complex systems
• linear response
• liquid crystals

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.