In reply to [EMAIL PROTECTED]'s message of Sat, 23 Feb 2008 11:34:12 EST: Hi Frank, [snip] >Bose Condensate? , AFAIK, they form just above absolute zero. Why were you >expecting one to form? > >Good comment. A Bose condensate of electrons only forms at low >temperatures. I was attempting to form a Bose condensate of protons (also >known as an >inverse condensate). The thermal velocity of protons is much less that the >thermal velocity of electrons at room temperature. This lower velocity is a >result of the increased mass of the protons. The distribution of the kinetic >energy of particles with differing masses is the same. I even tried helium >in >a past experiments in an attempt to obtain an even lower thermal velocity. I >believe that protons in a proton conductor may be forced to condense through >external stimulation. The required stimulation depends on the coherence >length. The product of the length of coherence and frequency is 1.094 >meghertz-meters.
Assuming your coherence length is at least proportional to the De Broglie wavelength (L_DB) and L_DB = h/p and p = sqrt(2*m*E) where E = kinetic energy, we get L_DB = h/(sqrt(2*m*E)) . Since, as you state above, the energy is "the same" irrespective of type of particle, we see that L_DB is in fact shorter for heavy particles than it is for light ones (the mass is in the denominator). IOW I would expect the coherence length of electrons to be sqrt(1836) ~= 43 times greater than that of protons. IOW I think your quest for heavier particles may be misguided. >If your intent is to increase the strength of the phonons, why not use sound >for >the stimulation, i.e. attach an ultra-sound generator to the wire, and >stimulate >it at the desired frequency? It may be easier to tailor the length of the >wire >to the frequency of the generator than the other way around. (start with wire >that is a little too long, then you can slowly reduce it to the correct size >- >perhaps even using an adjustable clamp to change the natural frequency - as >with >a violin or guitar). > >Another good comment: > >I like this idea. In general, applying shock to a Bose condensate of >protons is what I want to do. The required frequencies for the lengths of >wire I >am working with are in the 10 megahertz range. I have no way to mechanically >stimulate a proton conductor at 10 megahertz. Piezo-electric crystals have been used in the past, to achieve sonic frequencies in a solid on the order of 10 GHz (in the most extreme case of which I am aware), so I think 10 MHz should be well within the realm of possibility. >I would like to do this. It >would take one tight guitar string. In my previous post I suggested that the natural resonant frequency was significant, which isn't necessarily so. It would be difficult to achieve, since this is determined by the speed of sound in the material in question, whereas the frequency you are striving for is determined by your 1 MHz-m product, which as I have pointed out before, is actually a velocity (about 1E6 m/s). The speed of sound in most metals is on the order of 4000 m/s, so there is an implicit mismatch here. If you really want to resonate the wire at a natural resonant frequency of the wire, then perhaps you can find a metal-temperature combination where 1E6 m/s is a whole multiple of the speed of sound in the metal. This may be a matter of slowly heating the wire (passing a current through it?), until the right sound velocity in the wire is reached. (Assuming that there is some temperature dependence of sound velocity in a metal.) [snip] BTW, while researching this response, I came across a reference to the "Fermi velocity of electrons" (see http://scienceworld.wolfram.com/physics/FermiVelocity.html), which I note is very close to your 1 MHz-m product. Regards, Robin van Spaandonk The shrub is a plant.
