From Neural oscillation - Wikipedia:

Oscillatory activity in the brain is widely observed at different levels of organization and is thought to play a key role in processing neural information.

In general, is there a relation between large-scale oscillations and small-scale oscillations? How are the "larger" ones created from "smaller" ones? I think it must relate to coupled oscillations in small-scale, is that correct? Does it behave like the creation - annihilation in quantum mechanics? How would one describe all the large and small ones in one framework?

Related: Is there a difference between physiological stimulations and psychological stimulations?

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    $\begingroup$ I'm voting to close this question as off-topic because this seems to be about Neuroscience and might be migrated to the appropriate SE. $\endgroup$ – StephenG Apr 20 '18 at 4:44
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    $\begingroup$ No, that's just an example on small-scale and large-scale oscillations. One can generalize it to ecology, climatology, astronomy, etc. $\endgroup$ – Ooker Apr 20 '18 at 4:53
  • $\begingroup$ My view is that there will be people on the Psychology & Neuroscience SE who understand you question and will actually have considered what you're asking. But in all honesty even if I though this was physics, as written the question seems far too broad or possibly opinion based. $\endgroup$ – StephenG Apr 20 '18 at 4:57
  • $\begingroup$ If possible, can you introduce me some topics relate to this so I can ask more specific questions? Most results I found go too much in details of the system in analysis. $\endgroup$ – Ooker Apr 20 '18 at 5:42
  • $\begingroup$ If you want resources I'd suggest closing this question and opening a new one as a specific request for resources (there is a tag for that) for one specific subject area. Indicate in the question your level of knowledge (e.g. maths comfort zone, physics comfort zone). $\endgroup$ – StephenG Apr 20 '18 at 5:55

Yes, there is. The keywords you're looking for are collective behavior and, in particular, synchronization in dynamical systems. And yes again: there must be some sort of coupling and, in a discrete model, the coupling between the individual oscillators will typically take the form of a synchronization network.

A recent (2015) review is Synchronization of chaotic systems, by Pecora and Carroll, and probably also worth mentioning are the book Dynamical System Synchronization by Luo and the highly-cited 2002 review The synchronization of chaotic systems by Boccaletti et al., but there's plenty of material on-line.

The last two questions are most interesting and unfortunately I can answer little more than to say that, yes, I think there might be a field theoretical approach to the problem, but all I could find in a quick search is the work of Ovchinnikov on Topological field theory of dynamical systems (paper II) (arxiv I, arxiv II).

  • $\begingroup$ so the large-scale oscillations are just synchronized oscillations of components? $\endgroup$ – Ooker Apr 21 '18 at 10:21
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    $\begingroup$ That is an important mechanism, especially in the context of complex systems, but the question is very broad, so the answer is probably "no". :-) You'll have, e.g., situations where the large-scale oscillations are unrelated to the small-scale ones: a pendulum oscillations can be unrelated to sound propagating through its body, which is in turn unrelated to the random thermal lattice vibrations of its material. $\endgroup$ – stafusa Apr 21 '18 at 10:33
  • $\begingroup$ yes, I am wondering what is a large-sale oscillation. For example the pendulum, it can be though as a single oscillation, but surely it can't be the elemental oscillations from standard model, right? I don't know how the oscillation of the atoms constitute the oscillation of the pendulum. $\endgroup$ – Ooker Apr 21 '18 at 11:02
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    $\begingroup$ No, I wouldn't say that. The point is that "large-scale oscillation" isn't a technical term, it lacks a precise definition, so it'll be a matter of interpretation what it corresponds to in a given system. $\endgroup$ – stafusa Apr 21 '18 at 13:35
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    $\begingroup$ No, I woudn't say "absolutely". Actually, if you, for example, have LSO's arising from SSO through synchronization, then there's clearly a relation between both. Another example are turbulent flows, which can be seen as transporting energy through different scales until it's dissipated at microscopic scales. And yes, "large" and "small" are context dependent. It might be easier to say more if you have a concrete situation - as it is, it's unavoidable to be vague, because the context is too broad. $\endgroup$ – stafusa May 18 '18 at 13:20

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