Talk:Bose-Einstein condensate
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An event mentioned in this article is a June 5 selected anniversary
Bosonic statistics allows for many particles to have the same quantum numbers. However, at normal temperatures, the distrobution of particles is shared over many energy levels. Bose condensation occurs when a macroscopic (from a thermodynamic point of view) number of particles are in the ground state. A superconductor can loosely be thought of as a bose condensed state of electrion pairs, but this is heuristic only. Superfluidity does not necessarily occur with bose condensation. The easiest way to see this is that in bose condensation the ground state is at zero momentum. Superfluidity is the absence of viscosity, where, if given an initial velocity, there is no mechanism for the degredation of this velocity. Landau realized that the extra ingredient needed was a minimum in the energy dispersion relation, where the particles could then exists at finite velocity in a macroscopically coherent state.
In the first paragraph, in the parenthetical statement about Fermi-Dirac Statistics, the word "pearl" is used. Is this a typo? Should it be "particles?"
-> yes i think so, i just made this change
"A Bose-Einstein condensate was not actually created in a lab until June 5, 1995,"
Isn't Helium II a Bose-Einstein condensate? This has been created much earlier. If anyone knows in what way a superfuid is not considered a BEC it would be a good idea to clarify this statement.
--> AFAIK the major difference is that BEC occurs without any interactions between the particles, and is due to a rather simple balance between entropy and single particle energies. In He II the interactions are crucial to the phase transition. It would be nice to have an explanation of the opiginal Bose-Einstein derivation of the transition temperature. I might try to write one up later on.
- --> The theory of a BEC as described by the work of Bose and Einstein is for a gas of non-interacting bosons. The superfluid Helium of P.Kapitsa can only be seen as an (strongly) interacting analogon for BEC. In Helium there is something like a 10% of the particles that can become superfluid, while non-interacting Bose-gas BEC's have no depletion whatsoever and interacting Bose-gas BEC's have only a very small depletion. To make life complicated bare in mind is that an interacting bose-gas condensate has superfluid(N.N. Bogoliubov proved this in 1947 IIRC) properties, but this doesn't mean a superfluid is a BEC. A BEC is caused by the statistics and only influenced by the interactions.
The derivation of the transition temperature isn't that hard(in a uniform potential). In D-dimensions one finds for the amount of particles (N) allowed to live in excited states:
<math>N=(\frac{L^2 2\pi m k_B T_c}{h^2})^{D/2}\sum_{k=1}^{\infty}{\frac{1}{k^{D/2}}}<math>
in 3D this gives a critical temperature
<math>T_c=(\frac{n}{\zeta(\frac{3}{2})})^{2/3}\frac{h^2}{2\pi m k_B}<math>
with n=particle density
h=planck's constant
<math>k_B<math>=Boltzman constant
<math>\zeta<math>= the Rieman zeta-function
The moment I start the Dutch article about BEC, I'll add some things here.
- Disagree. The BEC is a name for phenomenum when bose-particles get accumulated in the base state in macroscopic quantities (as written in Landau-Lifshitz, vol. V, paragraph 62). The wave function of the condensate is supefluid and parameter of order. I don't undestand why you think that BEC is something can happen only with noninteracting gas. OK, suppose BEC is for gases only - then how do you call accumulation of particles in the base state? --GS 02:57, 7 May 2005 (UTC)
- (only second arrow is my opinion) Yes you are right when you say BEC is a phenomenon where a macroscopic amount of particles reside in the groundstate. And you are also right when you say that a BEC has the superfluid property...but I believe it is wrong to conclude the other way around: namely that a system that is superfluid is a BEC, this is not necessarily true.(something like saying: birds can fly => everything that can fly is a bird).
- I also didn't say a BEC is only something that can happen in a noninteracting gas. What I wrote was that the work of Bose and Einstein predicted BEC for a non-interacting gas. It is quite simple to show that this specific quantum phasetransition is caused purely by the used statistics, not the interactions. The interactions influence the transition by causing a depletion of the groundstate, but this depletion is very small(only a few % at most).
- I only said that superfluid HeII isn't a BEC, this is because the transition happens at temperatures wich are much to high (eg order 1000x higher then expected), with hugh depletions(>90%) and in a strongly interacting system. The cause of the "condensation to the groundstate" is different that is why it shouldn't be called BEC.(Dutch article (http://nl.wikipedia.org/wiki/Bose-Einsteincondensatie))--Shade² 12:23, 12 May 2005 (UTC)
- There is no 'cause', there is only possibility to condensate. Temperature (in other words - energy per molecule) works against the tendency. Interaction... could work both directions depending on. The attraction between He atoms, most likely, is responsible for the critical temperature 'too high'. The depletion of 90% - I don't know what you mean, AFAIK density of superfluid in He goes to 0 as T goes to 0 (see google://"He superfluid normal component density").
- You do agree with you that there is a "condensation to the groundstate" of the Bose-particles of He-4. --GS 18:14, 12 May 2005 (UTC)
- Depletion of 90% means that at most 10% of the particles in He can become superfluid, while there are no restrictions(ie all particles condense) in the classical non-interacting theory and with interactions only a few percents remain in the excited states.
- Is not in agreement with experiments. See, f.e. http://mxp.physics.umn.edu/s03/Projects/S03He/theory.htm --GS 17:36, 13 May 2005 (UTC)
- Superfluid HeII isn't only in He-4(bosons) but also in He-3(fermions)...I do agree that there is a condensation to the groundstate but the underlying mechanism is different as far as I know. BEC=statistics, superfluid HeII=interactions. So, though the endresults look the same they might be considered different things.--Shade² 11:34, 13 May 2005 (UTC)
The second paragraph contains this statement: "the many overlapping atoms can be considered to be a single super-atom". I don't think this is a very precise way of describing it. The atoms are all in a single state, but they have not formed one particle ("super" or otherwise) in any way. Could someone come up with a better way of putting this?
Though there does not seem to be an entry in this encyclopedia for it, "Superatom" is used interchangably with "Bose-Einstein condensate" to mean the same thing, so i think "superatom" is a very appropriate term.
Temperature error
Why does the 50 pK temperature given in the second sentence in this article, and repeated later on, conflict with the 450 pK "lowest temperature ever" given in the 1 E-12 K article?
Especially when the value here is for the first activity in this field, back in 1995.
Is it just that somebody didn't know the difference between "one twenty-billionth of a Kelvin" (in that improperly capitalized name originally in this article) and "twenty billionths of a kelvin"? The former is 0.05 nK; the latter is 20 nK. I suspect that those two appearances in this article should read 20 nanokelvins. Gene Nygaard 03:20, 17 Dec 2004 (UTC)
Something is Missing!?
can anybody add what is meant by Tc and m, just to be precise. look at the formula. you will know what i mean. --212.202.37.226 23:49, 5 Jun 2005 (UTC)jan girke
- ok, its fixed. PAR 01:27, 6 Jun 2005 (UTC)