Can anyone explain the significance of the formation of a fermionic
condensate in the laboratory?
What should that be? You can have condensates only for integer spin.
For fermions this requires pairs of fermions - see superconductivity.
> Can anyone explain the significance of the formation of a fermionic
> condensate in the laboratory?
The recently announced fermionic condensate
(http://www.colorado.edu/news/reports/fermions/) just like the bosonic
condensate that was realized a few years ago was predicted by theory long
ago. The fact that these experiments can actually be realized is a
confirmation of theoretical predictions, and that's always good. At least
it makes the theorists happy. :-)
More specifically, the reason fermions were able to condense is that they
formed bound pairs (Cooper pairs) that act like bosons and can condense
like other Bose-Einstein condensates. What's interesting about Cooper
pairs is that properties of a superconductor are explained by the presence
of a condensate of Cooper paired electrons. This theory of
superconductivity (BCS theory) has many predictions that have been
verified and that can be seen as indirect evidence of the presence of an
electron condensate, however this condensate has not actually been
directly observed. So condensation of fermions in a controlled laboratory
setting gives us a chance to study this state of matter directly rather
than indirectly as before. The more we know about Cooper pairs, the
more we know about superconductors, and that makes everyone happy. :-)
As for the technological applications, I'm not really aware of any. And if
there were, they would be impractical for a while since these condensates
require the lowest temperatures ever achieved on Earth.
Hope this helps.
Basically, there had been two known ways of getting fermions
to form pairs, which act approximately like bosons, and can thus
"condense" - meaning that a whole bunch of them get into the same
One way was for the fermions to literally stick together: for
example, some protons, neutrons and electrons (all fermions)
can stick together and form helium-4, which is a boson... and
these bosons can then form a condensate known as "superfluid helium".
A fancy way of saying that the fermions stick together is to
say that they have strongly correlated POSITIONS: if you know
where one is, you've got a good idea where its mates are.
The other option was for the fermions to get strongly correlated
MOMENTA. The classic example is a superconductor, where electrons
form "Cooper pairs", which are bosons. The two electrons in a
Cooper pair aren't close together in position, but their momenta
In more mathematical terms: their wavefunctions don't look like two
nearby bumps, but the FOURIER TRANSFORMS of their wavefunctions do.
The new "fermionic condensate" allows physicists to interpolate
between these two extremes: they can now get some fermions to
correlate in ways that are "between" position correlation and
momentum correlation. Even better, they can adjust the type of
correlation by changing an external magnetic field.
It's not surprising that the media are having a tough time explaining
> The other option was for the fermions to get strongly correlated
> MOMENTA. The classic example is a superconductor, where electrons
> form "Cooper pairs", which are bosons. The two electrons in a
> Cooper pair aren't close together in position, but their momenta
> are close.
> In more mathematical terms: their wavefunctions don't look like two
> nearby bumps, but the FOURIER TRANSFORMS of their wavefunctions do.
The momenta of electrons in so called "Cooper pair" are opposite.
Therefore FOURIER TRANSFORMS of "Cooper pair" wavefunction are two far
bumps. As for other superconductivity theories, for
example[http://uk.arxiv.org/abs/cond-mat/0309516v2], momenta of
electrons in the pairs involved there are close. Strictly speaking,
the paired electrons are also close together in position. Though
paired, electrons can't form the Bose condensate due to the Pauli
principle in distinction from BEC versions of the superconductivity
Original BCS Hamiltonian can't satisfy the requirements of the
gradient invariance of the electromagnetic interaction due to the
specific form of the interaction terms. The gradient invariance can be
satisfied in the BCS theory only by means of the Gor'kov's
transformation which, in fact, accounts for only diagonal terms and
the interaction terms with the "BCS structure", that is connecting
zero momenta pairs. Other interaction terms are excluded from the
analysis due to the incorrect treatment of the Hartree-Fock procedure
involving the existence of the "anomalous averages" of the
superconductivity wave function.
The suggestion of the existence of anomalous averages leads to
contradictions. It was shown in our study
[http://uk.arxiv.org/abs/cond-mat/0309516v2], that these anomalous
averages for real systems, satisfying the requirements of gradient
invariance, may be represented merely in the form of a series, whose
expansion parameter infinitely increases with the size of the system.
Therefore violatation of the formal logics in the BCS theory becomes
This fact should be accounted for in consideration of the properties
of the "Fermionic condensates".
Sincerely, Igor Yurin
"John Baez" <ba...@galaxy.ucr.edu> wrote in message
I would like to know what is the opinion of knowledgeable people about the
theory / "theory" / "model" / dream / @#+!!?%$ (underline appropriate
according to your view) of Laurent Nottale.
For those who have never heard...:
It is about a "generalized special relativity" to systems related not only
by inertial movement, but also by rescaling. The author, quite prolific for
last 10 years, concludes that all his stuff implies a fractal structure of
space-time, and derives ("derives"???) plenty of things, such as cough,
cough, quantum physics... Concretely, from the non-differentiability of
trajectories within such a nervous substrate as is the fractal space, he
derives a kind of stochastic process, and by some manipulations I could not
follow, he rederives something equivalent (?) to Nelson's stochastic approach
to quanta. Hence, the Schrodinger equation, etc.
Then he claims to get everything. Electron and other masses derived from
charges. Unification of all couplings at the Planck scale. Some astrophysical
consequences at mid-cosmological/astronomical scales [Nottale worked in
an astronomical observatory at Meudon], etc. etc.
To make it short, a theory of almost everything...
Now, the problem is that by a superficial surfing of the Web you find
a lot of advertisements, including self-..., and also some harsh words, but
without any thorough analysis. One of my friends have just said: "All this is
just French Science, and if you don't know what it is, read Sokal..."
Would anybody say something serious on all this?
(But, if I may, please avoid the statement I have heard already 10 times:
"I don't know much about it, so it is not normal, sane physics, otherwise
everybody would know it. So, by default it is worthless" )
You should provide a link to one of his self-published papers (I am
betting that nothing has made it to a peer-review journal, a warning
I happen to be a bit of a fringe-scientist magnet myself. The most
common thing I find are many claims and words, no math. I have a
simple policy that is I see only text, no equations, I don't buy a
thing the person is saying.
If there are any derivations, then a program like Mathematica should be
able to step through it. At this time, I have yet to see a worker on
the fringe use an analytic math program (Maple and Mathworks are
others). One needs to be precise enough for a machine to understand,
and that is far too high a bar for most folks. By the way, I have
solved over 50 problems in special relativity using Mathematica, so I
know special relativity can be done with that tool. I did that with a
non-standard approach, but that is just me being a fringe magnet :-)
Another quick screen for validity is to search for words like
"Lagrangian" and "action." I have yet to see a person who promises a
new structure use them. These words tie into so much confirmed
physics, from EM to the standard model, that one should not ignore them!
If you find a document on the web, do a quick scan for equations and
those two words. If it passes those two tests, send me the URL and I
will continue the discussion outside the group. The nice thing about
this kind of test is that it is unbiazed and quick to do.
> I would like to know what is the opinion of knowledgeable people about the
> theory / "theory" / "model" / dream / @#+!!?%$ (underline appropriate
> according to your view) of Laurent Nottale.
> Now, the problem is that by a superficial surfing of the Web you find
> a lot of advertisements, including self-..., and also some harsh words,
> but without any thorough analysis.
Apparently J.Cresson has done some work on the underlying maths, see:
which seems to have appeared in J.Math.Phys. in 2003:
Thomas Sauvaget wrote:
> Jerzy Karczmarczuk wrote ...
>>I would like to know what is the opinion of knowledgeable people about =
>>theory / "theory" [ ...] of Laurent Nottale.
> Apparently J.Cresson has done some work on the underlying maths, see:
> which seems to have appeared in J.Math.Phys. in 2003:
Cresson cites Nottale, and says that some of his math has been inspired
by it. Still, I can't deduce the physical status of this stuff...
Mathematics is a harsh, but sometimes surpisingly tolerant mistress.
One can play with fractal spaces, "scale covariant derivatives", etc.,
but what all that has to do with, say, Quantum infrastructure?
And this is what I would like to know... I can understand that weakening=
some mathematical properties of classical trajectories, making them "wigg=
around" may lead to equations like Langevin's, with some associated stoch=
process. But it is known that the process which would give the Schr=F6din=
equation must have some bizarre non-localities.
Cresson says that he "gets nonlinear Schr=F6dinger equation from Newton
equations". Hm. For what, for the action? Anyway, what about simpler thin=
the Bell inequalities for example. It is possible to derive this stuff fr=
some fractal space as well?
> Cresson cites Nottale, and says that some of his math has been inspired
> by it. Still, I can't deduce the physical status of this stuff...
> Mathematics is a harsh, but sometimes surpisingly tolerant mistress.
> One can play with fractal spaces, "scale covariant derivatives", etc.,
> but what all that has to do with, say, Quantum infrastructure?
> And this is what I would like to know...
I'm sorry, I just cited this because you said "by a superficial
surfing of the Web you find a lot of advertisements, including
self-..., and also some harsh words, but without any thorough
analysis". I mistakenly interpreted "thoroughly" to mean "rigorously",
and thought this reference would help. Now you meant "physical
relevance", so I would guess either they make testable predictions or
they don't. If they did make some (I'm not familiar at all with their
works), then it might be useful to cite one or two explicitely, and
see what specialists think.