What is a mean field approximation please?

>>8517237
Sorry, I've never heard of a "mean field approximation please".

>>8517257

what's wrong with you?

>>8517237
Imagine you have lots of shit all contributing to a particular phenomenon, it'd be a pain in the balls (and perhaps intractable) to handle all the components individually so instead you take some dominant components of each field and you just average then together and hope for the best.

>>8517271

are there systematic ways in which people decide on those components?

>>8517271
so chaos theory?

>>8517237
So you have a bunch particles all interacting with each other via a field. If you have N particles, then particle 1 interacts with particle 2, 3, ... and so forth, so it's pretty complicated as every particle interacts with every other particle, that changes all of those particles, which changes how they interact etc etc. If you were to write all those interactions down you'd end up with N! terms (including the particle itself), which obviously gets pretty fucking huge pretty fucking quickly.

Mean field theory is basically the idea that there is an equilibrium state. The state of the particles then only slightly deviates from that equilibrium, so little that it doesn't influence the field enough to change it significantly. As the overall field is constant, you can just ignore the individual interactions between the particles and only look at the big picture (i.e. the sum of all fields in average). Then you can look at every particle without looking at N-1 other particles and everything becomes very simple.

This is of course not always a good way to solve many particle problems. E.g. it might be a good idea to approximate the behavior of a crystal, but it's probably a bad idea to apply it on a gas.

>>8517309
so pop-sci retard?

>>8517358
it was a joking comparison you braindead faggot

It's an approximation for the mean of a field

>>8517381
/thread

>>8517368
>i-i-i was just pretending

>>8517402
>What is satire and sarcasm on the internet

>>8517412
I think you need to ask yourself that question friend.

>>8517237
It is when you alter a field so that it is approximately mean.