Unraveling the Mystery of Quantum Fluids: A Look into Superfluidity Theory

[StevieTNZ]

Is there a complete theory for quantum fluids (superfluidity) now?

In this book (published 1990) it says "Because of the dominant importance of quantum mechanics for He II that fluid is called a quantum fluid. Its theory is still not completed today. Certain features can still not be accounted for quantitatively."

 

[ZapperZ]

Is there a complete theory for quantum fluids (superfluidity) now?

In this book (published 1990) it says "Because of the dominant importance of quantum mechanics for He II that fluid is called a quantum fluid. Its theory is still not completed today. Certain features can still not be accounted for quantitatively."

What book is that? When you are referring to a source, please be as specific and detailed as possible. If you cite a paper, include proper citation with the name of the author, journal name, volume, page, and year. If you are citing a book, include the name of the author, title of the book, publication date, and publisher.

While this is still a forum, we try to maintain a higher standard than other forums on the net, and requires proper citation as close to actual scientific publication as possible.

To answer your question, it would be rather silly that several Nobel Prizes have been given for theoretical description of superfluidity, including the one given to Tony Leggett for He3, if we don't have a proper theory for it. The term "completed" is vague. Does that fact that we don't have a complete solution to the classical 3-body problem implies that classical Newtonian physics is "incomplete"?

Zz.

 

[nnnm4]

It's still accurate to say that we don't have a complete theoretical description of superfluidity in He4. Superfluidity in he3 and conventional superconductivity are described well with bcs type theories

 

[genneth]

It's still accurate to say that we don't have a complete theoretical description of superfluidity in He4. Superfluidity in he3 and conventional superconductivity are described well with bcs type theories

This is a strange answer. In condensed matter we never have a complete description --- the whole point is to *not* have a complete description! I second Z's answer --- the OP needs to be more specific about where the quote came from, and what it refers to.

Also, I would strongly disagree with "conventional superconductivity are described well with bcs type theories" --- those theories (as everyone is aware, I hope) are neglecting some reasonably important things for practical applications --- the role of disorder, magnetism, strong phonon-coupling, multi-band effects, etc. BCS is useful as an educational tool, but for real things people use a "more complete" description.

 

[nnnm4]

What I mean to say, and perhaps I'm mistaken, is that BCS theory is a theory which can make quantitative predictions of the superconducting gap, for example. Is there a similar predictive quantitative theory for superfluid helium-4? The two-fluid model is phenomenological, so I was thinking of something more "first-principles" than that.

 

[ZapperZ]

Also, I would strongly disagree with "conventional superconductivity are described well with bcs type theories" --- those theories (as everyone is aware, I hope) are neglecting some reasonably important things for practical applications --- the role of disorder, magnetism, strong phonon-coupling, multi-band effects, etc. BCS is useful as an educational tool, but for real things people use a "more complete" description.

One needs to be a bit careful here. In condensed matter, one often refers to "BCS theory" not as solely the theory that came out of the 1957 paper, but rather the whole general theory of conventional superconductors. The same way one doesn't refer to Special Theory of Relativity as just the Einstein's 1905 paper, the BCS theory has evolved, and this has been extended to include other issues, such as strong-coupling, etc. So when one says that BCS theory may not work for, say, high-Tc superconductors, one is referring to a more generalized form where the standard electron-bosonic interaction forms some sort of the glue for paring. You will note that scenario such as electron-spinon (or other magnetic spin fluctuations) coupling have often been used within the BCS scenario, despite the fact that the original BCS theory explicitly used phonon coupling.

So the reference to "BCS theory" isn't simply the 1957 theory, but rather the "philosophy" (for lack of a better word) of the theory.

Zz.

 

[genneth]

One needs to be a bit careful here. In condensed matter, one often refers to "BCS theory" not as solely the theory that came out of the 1957 paper, but rather the whole general theory of conventional superconductors. The same way one doesn't refer to Special Theory of Relativity as just the Einstein's 1905 paper, the BCS theory has evolved, and this has been extended to include other issues, such as strong-coupling, etc. So when one says that BCS theory may not work for, say, high-Tc superconductors, one is referring to a more generalized form where the standard electron-bosonic interaction forms some sort of the glue for paring. You will note that scenario such as electron-spinon (or other magnetic spin fluctuations) coupling have often been used within the BCS scenario, despite the fact that the original BCS theory explicitly used phonon coupling.

So the reference to "BCS theory" isn't simply the 1957 theory, but rather the "philosophy" (for lack of a better word) of the theory.

Zz.

That is a good point.

However, to nnnm4 I would like to point out that it is still be bit far to call BCS actually predicting the superconducting gap --- it predicts a certain set of relations between things (e.g. superconducting gap vs. critical temperature) but since the "microscopic" input parameters are not really independently determinable, I would not say that we "understand" superconductors better than liquid He-4 (or He-3).

 

[guyingfei]

I think superfluid is clear known, but quantum fluids is a much 'wide' concept.
quantum fluid= interacting atoms or electrons without long range order?

 

[ZapperZ]

I think superfluid is clear known, but quantum fluids is a much 'wide' concept.
quantum fluid= interacting atoms or electrons without long range order?

Well, that definition doesn't quite work, because "superfluidity" and "superconductivity" are examples of phenomena of "quantum fluid", and they have long-range orders.

To me, quantum fluid is a quantum many-body interaction of a correlated systems, typically electronic systems. This, therefore, covers a wide range of phenomena, and includes also many-body theories such as BCS, Fermi Liquid, etc.. etc.

One can see a summary/list of such things here:

http://web.mit.edu/redingtn/www/netadv/Xqufluid.html

Unfortunately, in this discussion, the OP seems to have gone AWOL, so it is hard to figure out what exactly is being asked here.

Zz.

 

[arielleon]

Thanks zz, my definition is wrong. I think what I described is "quantum liquid" rather than fluid
but i still don't know the definition of qfluid
What's the difference between fluid and liquid?

 

[guyingfei]

Sorry, I misuse my friend arielleon's account.
That's me

 

[jetwaterluffy]

Thanks zz, my definition is wrong. I think what I described is "quantum liquid" rather than fluid
but i still don't know the definition of qfluid
What's the difference between fluid and liquid?

A fluid is anything that flows, which can include gases, liquids, and plasma. http://en.wikipedia.org/wiki/Fluid However, seeing as a "quantum fluid" apparently includes superconductors, it must mean something else.

BTW, I heard somewhere that you can't predict what materials can become a high-temperature superconductor, you have to cool them down and see. (I think this was in some issue of the new scientist). Is this true, and if so, why not?

 

[cgk]

BTW, I heard somewhere that you can't predict what materials can become a high-temperature superconductor, you have to cool them down and see. (I think this was in some issue of the new scientist). Is this true, and if so, why not?

In general this is true. In fact, even for conventional superconductors you would have a very hard time coming up with quantitative first-principles theoretical predictions about their conductance behavior. (In fact, this even applies for even much simpler electronic systems and simpler electronic properties than conductance).

There are really two kinds of fundamental problems:
1) While it is perfectly possible to write down the microscopic equations which govern the electronic structures of such systems (at the atomic level), those equations are too complex and involve too many degrees of freedom to be solved with any brute force method. E.g., superconductors will involve long range order, and you cannot simply calculate the wave function of an 1mm x 1mm x 1mm block of material, because it contains too many atoms. Thus, in order to make predictions, you generally need to assume a simplified model (e.g., some kind of generalized Hubbard or Anderson model) and then determine the parameters of that model.
2) The mechanisms which can lead to superconductivity are neither known comprehensively, nor fully understood[*]. Both of those are prerequisites in order to be able to definitely tell whether and where a material will undergo a phase transition to the superconducting state. If you miss certain possible mechanism of superconductivity, you have no way of ever finding it because you don't know what to look for!

[*] In practice that would mean that you need to know *all* possible physical models which can exhibit superconducting behavior, and then somehow try to understand whether a given material fits to that model.

 

[Minich]

Is there a complete theory for quantum fluids (superfluidity) now?

In this book (published 1990) it says "Because of the dominant importance of quantum mechanics for He II that fluid is called a quantum fluid. Its theory is still not completed today. Certain features can still not be accounted for quantitatively."

Let me quote Peierls.

[898] Rudolf Peierls to Nevill Mott
Oxford, 11.5.1991
(carbon copy)
Dear Nevill,
Thank you for your letter.1329 I know of course, of your idea that in
High-Tc substances there are pairs above Tc. When we met at Harwell,
it occurred to me that it should be possible to test this by looking at
a Josephson function between a high-Tc substance above its Tc and a
conventional superconductor. Do you agree that this is right? If so
should one urge that this be tried?
I do not know the answer to your question whether a Bose liquid
could fail to be a superfluid at T = 0, because I do not understand,
and tend to distrust, realistic theories of superfluidity. My guess would
be that for strong purely repulsive forces this should be possible, but I
have no arguments.
Yours sincerely, Rudolf Peierls

From the book by Sabine Lee
Sir Rudolf Peierls Selected Private and Scientific Correspondence Vol.2

Red selected by Minich
I know the V. Ginzburg (Nobel Prize winner 2003) saying that for He4 the theory analogous to BCS does not exist. So did Feynman asked everybody, who could get formula for heat capacity of He4 near λ point, publish it (Kikuchi's he considered to be wrong)!

As i know nobody could get formula till now (2012 january) :)

Landau never recognized, that bose einstein condensation means superfluidity :)