17 views

Skip to first unread message

Jan 30, 2004, 8:53:38 AM1/30/04

to

Can anyone explain the significance of the formation of a fermionic

condensate in the laboratory?

Feb 2, 2004, 4:58:29 PM2/2/04

to

Dactyl49 wrote:

> Can anyone explain the significance of the formation of a fermionic

> condensate in the laboratory?

> 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.

Arnold Neumaier

Feb 2, 2004, 4:59:09 PM2/2/04

to

On Fri, 30 Jan 2004 08:53:38 -0500, Dactyl49 wrote:

> 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.

Igor

Feb 2, 2004, 4:59:35 PM2/2/04

to

The media have been talking in very vague terms about the

new "fermionic condensate"; here's an article that's a bit

clearer:

new "fermionic condensate"; here's an article that's a bit

clearer:

http://www.aip.org/enews/physnews/2004/671.html

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

state.

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

are close.

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

this!

Feb 3, 2004, 8:11:07 AM2/3/04

to

>

> 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

theory.

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

evident.

This fact should be accounted for in consideration of the properties

of the "Fermionic condensates".

Sincerely, Igor Yurin

Feb 5, 2004, 10:50:33 AM2/5/04

to

In both "extreme" examples, one can point at an interaction the glues pairs

of fermions together. The helium nucleus is bound by strong forces, Cooper

pairs are bound by phonons. What is the force that binds fermions in this

new condensate? Is it van der Vaals force?

of fermions together. The helium nucleus is bound by strong forces, Cooper

pairs are bound by phonons. What is the force that binds fermions in this

new condensate? Is it van der Vaals force?

"John Baez" <ba...@galaxy.ucr.edu> wrote in message

news:bvgqde$m45$1...@glue.ucr.edu...

Feb 5, 2004, 11:03:37 AM2/5/04

to

Dear Gurus,

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" )

Jerzy Karczmarczuk

Caen, France

Feb 7, 2004, 9:08:09 AM2/7/04

to

Hello Jerzy:

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

flag).

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.

doug

quaternions.com

Feb 8, 2004, 6:33:10 AM2/8/04

to

Jerzy Karczmarczuk <kar...@info.unicaen.fr> wrote in message news:<4020B95D...@info.unicaen.fr>...

> 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:

<http://arxiv.org/abs/math.GM/0211071>

which seems to have appeared in J.Math.Phys. in 2003:

<http://content.aip.org/JMAPAQ/v44/i11/4907_1.html>

--

thomas.

Feb 9, 2004, 5:44:23 AM2/9/04

to

Thomas Sauvaget wrote:

> Jerzy Karczmarczuk wrote ...

>=20

>=20

>>I would like to know what is the opinion of knowledgeable people about =

the

>>theory / "theory" [ ...] of Laurent Nottale.

>=20

>=20

> Apparently J.Cresson has done some work on the underlying maths, see:

> <http://arxiv.org/abs/math.GM/0211071>

>=20

> which seems to have appeared in J.Math.Phys. in 2003:

> <http://content.aip.org/JMAPAQ/v44/i11/4907_1.html>

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=

ling

around" may lead to equations like Langevin's, with some associated stoch=

astic

process. But it is known that the process which would give the Schr=F6din=

ger

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=

gs,

the Bell inequalities for example. It is possible to derive this stuff fr=

om

some fractal space as well?

Jerzy Karczmarczuk

Feb 11, 2004, 1:55:35 PM2/11/04

to

Jerzy Karczmarczuk <kar...@info.unicaen.fr> wrote in message news:<40276146...@info.unicaen.fr>...

> 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.

--

thomas.

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu