This was the topic of the Physics Colloquium today. It was interesting talk by Chris Vale. It was about how two-component Fermi gas can display universal properties at the cross-over between Bardeen-Cooper-Schrieffer state (a pair weakly correlated spin up and spin down electron form a Cooper pair in superconductors) and BEC state (a pair strongly correlated spin up and spin down electron form a boson). I.e. as you slowly increase the strength of the correlation you move from a BCS to BEC and somewhere in the middle (it was called unitary) weird things happen. Only a single parameter was needed to characterize this behaviour, called "the contact" because it is measure on how likely we can find a pair of particles at small separations.
Being a experimentalist, he bragged about how his team used Bragg's spectroscopy to probe the Fermi gas while varying the strength of interaction via Feshbach resonance (something I still don't really get, if someone is familiar with this tell me). Anyway, what other universal parameters do you guys know?
I think we just learnt one in class. (p.s. No Josh. You posted to many comments already =P).
I recall that the first time I learnt about the concept of universality was in a Phys2020 lecture Ross was giving ,where he emphasized several times on the universality near critical points. e.g. law of corresponding states-real gases at the same reduced volume and reduce temperature exert the same reduced pressure.
I like how the models we're learning are reasonably elegant, e.g. for this system, the contact, and for Drude model, only tau.
ReplyDeleteUniversality seems very useful in that you can create a standard method for comparison between stuff. Also, having the same number (so absence of units) for many objects would imply there is some physical significance in the constant.
I recall last year looking into the Kadowaki-Woods ratio, comparison between resistivity and conductivity. Something unsettling with this was the presence of units.
Another constant: Wilson ratio (magnetic susceptibility and heat capacity)
We could argue that universal constants are always around us, e.g. pi, e.
Bragged about Bragg spectroscopy...:D
Terrible pun...:). I get comments for this week though (and now I'm done!)!
ReplyDeleteI don't think that a universal constant need be unitless—I think it depends on the context. If the context allows it, you can define a characteristic unit, but since you'll only be comparing like quantities with the constant (e.g. metals in the Drude model, not tree height tau and electron scattering tau), I don't think that it is a necessary condition. Besides, you can always make it unitless with a small change. Of course, universal constants are always around us because they are universal!! They are there, even if we don't know about them :)! If you are paranoid about these sorts of things, then it is best to forget that point....
The Reynolds Number is an immediate example I can think of, from fluid dynamics. It essentially is a measure of all of the physical constants that are related to viscosity and is a scale for determining the relative scaling of various parameters (e.g. how viscous would a fluid be at length scale a compared with length scale b; like how viscous blood is in a capillary compared with blood in a flood drain... ignoring the fact that that is a lot of blood...). Of course, it is not for solid state. :)
For the Feshbach resonance: I think it has to do with the resonance between the bound state and the non-bound state in a system where the degrees of freedom of the state and the degrees of freedom of the reaction co-oridnates. So, essentially (Wikipedia tells me that) electrons (= fermions?) can form a bound state if an internal degree of freedom of the electrons is coupled to an external degree of freedom. So you can probe the Fermi nature of the electrons by moving them between a bound and unbound state. Shape resonance is the opposite of Feshbach resonance, and it seems to be when the electrons (or other things) keep the same boundness regardless of the external co-ordinates.
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