Can a cloud of electrons be stabilized by interactions between them?

[Suekdccia]

TL;DR Summary

Electrons tend to be repelled by electromagnetic interactions and cannit be attracted by gravity as it is a much weaker interaction. However, at low temperatures, can they be in a stable configuration by other interactions like magnetic ones or forming a Fermi liquid?

If you have many free electrons forming a cloud they wouldn't last too much as they would be repelled from each other due to electromagnetic forces. Gravity wouldn't help since it is much weaker than electromagnetic force, so electrons would still fly away


However, can they be stabililized by magnetic forces arising between electrons? Or perhaps, could they form a Fermi liquid [1] (at sufficiently low temperatures) that could interact with one another to form stable quasiparticles for an indefinite time (if no external perturbations exist) and that could in turn form also stable Cooper pairs as temperature approaches close to zero?

[1]: https://en.wikipedia.org/wiki/Fermi_liquid_theory

 

[Vanadium 50]

No.

 

[Suekdccia]

No.

Any info on why it's not possible?

 

[Vanadium 50]

I said to myself "don't answer him. Let him stew, Otherwise this is going to turn into the typical Suekdccia waste of time thread". But then I relented. My screw-up.

Some things to think about:

1. You need to put a modicum of effort in. Demanding that PF does all the work while you sit on your keester is deeply disrespectful.
2. Related to #1, show us a calculation. Don't simply demand we figure out whjere you are wrong.
3. How much repulsion do you need to add together to make it attractive?

 

[Suekdccia]

I said to myself "don't answer him. Let him stew, Otherwise this is going to turn into 5he typical Suekdccia waste of time thread". But then I relented. My screw-up.

Some things to think about:

1. You need to put a modicum of effort in. Demanding that PF does all the work while yuou sit on your keester is deeply disrespectful.
2. Related to #1, show us a calculation. Don't simply demand we figure out whjere you are wrong.
3. How much repulsion do you need to add together to make it attractive?

I'm simply asking whether it is theoretically possible to have, for example, electrons forming a fermi liquid if electrons' density and temperature are in the right range. If the answer is: This is impossible in all cases no matter what the conditions and no matter what calculations you do (like as if I asked if a proton can travel at beyond-speed of light velocities) then this thread is over. If there is a range of temperature and density in which this is possible then the thread is also over as I just need to know that. I've tried to search for an answer by myself and the only possibility that I've found is the fermi liquid one, but I'm not sure if my understanding of this is right. I just need someone wiser to correct me if I'm wrong and electrons could not form a Fermi liquid or any other stable state. I'm not asking anyone to do an abusive work load. I don't think it's necessary to tell me for the 5th time that all my threads are a waste of time. I understand the critics to the posts where I asked about speculative theories or where I added no references. But this time I'm referring to a question about the behaviour of matter according to our current models. If you personally don't like me and just want me to stop posting anything at this point just tell me and I will try to not post any longer as I don't want to annoy anyone, but please understand that if you just tell me "no" I would like to know why

 

[renormalize]

I'm simply asking whether it is theoretically possible to have, for example, electrons forming a fermi liquid if electrons' density and temperature are in the right range. If the answer is: This is impossible in all cases no matter what the conditions and no matter what calculations you do (like as if I asked if a proton can travel at beyond-speed of light velocities) then this thread is over.

You should study the consequences of the virial theorem (valid in both classical and quantum physics) as investigated in the context of plasma confinement. For example, from G. Schmidt, Physics of High Temperature Plasmas (2nd ed.), pg. 72:

This result is here motivated by plasmoids, but it is more broadly applicable: the virial theorem shows that any localized configuration of fields, charges, and currents cannot hold itself together by any self-forces. It will dynamically expand until it is constrained by external forces.

 

[Suekdccia]

You should study the consequences of the virial theorem (valid in both classical and quantum physics) as investigated in the context of plasma confinement. For example, from G. Schmidt, Physics of High Temperature Plasmas (2nd ed.), pg. 72:
View attachment 350218
This result is here motivated by plasmoids, but it is more broadly applicable: the virial theorem shows that any localized configuration of fields, charges, and currents cannot hold itself together by any self-forces. It will dynamically expand until it is constrained by external forces.

Thank you!

Just one question: would this apply to systems of any arbitrary size if they contain charges? For instance, electrons forming a Wigner crystal would be also destabilized by the theorem?

https://en.m.wikipedia.org/wiki/Wigner_crystal

 

[renormalize]

Just one question: would this apply to systems of any arbitrary size if they contain charges? For instance, electrons forming a Wigner crystal would be also destabilized by the theorem?

No, a Wigner crystal of electrons is stable because it is subjected to an external confining force field: a "uniform, inert, neutralizing background" like a lattice of positively-charged atomic nuclei, or an imposed magnetic field.