Talk:Bose–Hubbard model

Links

In an effort to make this readable to laypeople (or as close to laypeople as would be interested in the Bose-Hubbard model), I've tried to make sure any technical term is linked to an appropriate article. But I'm having a little trouble with "gap" and "superfluid susceptibility".

I searched Wikipedia for "energy gap" or "excitation gap", but couldn't find any article, so I linked to "band gap", which hopefully is close enough to what I mean. The point is, in the Mott Insulating state you normally have a certain number of particles, let's say one, on every site. However, with some energy the system can be excited to a state where one site is unoccupied (a hole) and one is doubly occupied. But the energy required must be greater than some non-zero minimum value. Thus, there's an "energy gap" between these states.

I also couldn't find an article on "superfluid susceptibility". Originally, the link was to susceptibility. This is a disambiguation page, but none of the choiced seemed to talk about superfluids. I linked it to the superfluid article, where perhaps something could be added about superfluid susceptibility.

The alternative, I guess, would be to red link to excitation gap and superfluid susceptibility until someone writes those articles.-- Tim314 (talk) 22:45, 18 March 2008 (UTC)

Black Holes

The article states "behaviour analogically similar to that of gravitational black holes and the expansion of the universe are also observed in the BEC described by this model". I haven't read the whole 232 page thesis that was linked to, but at one point it says:

Two of the themes that have emerged from the field of ultra-cold Bose gases are: (A) Quantum phase transitions in highly correlated systems; and (B) Analogue models of gravity. This thesis consists of three theoretical studies, logically divided between the two themes as follows: Part I: A phase-space method for the Bose-Hubbard model (theme A); Part II: An analogue model of an expanding universe in Bose-Einstein condensates (theme B); and Part III: An analogue model of an acoustic Black Hole in Bose-Einstein condensates (theme B).

It seems like maybe the author first did some calculations with the Bose-Hubbard model, and then did some separate calculations involving BEC's and anaglogue models of gravity. It's not atypical for a physics Ph.D. student to have worked on a few loosely related projects and then have to combine them into a single thesis. But if the Bose-Hubbard model wasn't actually used in studying black holes and universal expansion, then that sentence should probably be removed from the article. -- Tim314 (talk) 23:07, 18 March 2008 (UTC)

Also, I don't think high-energy physicists have actually created mini-black holes, nor so far as I know are they trying to do so. I've read various speculation in the press that high energy experiments like the LHC could create mini-black holes. But it's not clear that they would, nor is that the goal of the experiments. Usually it's brought up as an "Oh-my-gosh, could this destroy the world?" type of thing. (Answer: No, because (A) such black holes are expected to evaporate almost instantaneously, and (B) if we could destroy the world in this way, the much higher energy collisions that happen when cosmic rays hit our atmosphere would have already done it.) So unless someone has a reason not to, I'm inclined to remove the bit about high-energy physicists, even if the part about the Bose-Hubbard model being used to study black holes turns out to be accurate. --Tim314 (talk) 23:14, 18 March 2008 (UTC)

UPDATE: It's been over a week since I posted the above comment and I haven't received a response, so I went ahead and removed the paragraph on black holes. It still think (1) that thesis wasn't really using the Bose-Hubbard model in the portion dealing with black holes, and (2) the article was incorrect in claiming black holes are studied by high-energy physicists in particle accelerators. See my above comments for more detail. -- Tim314 (talk) 21:04, 27 March 2008 (UTC)

correct Hamiltonian?

Is the first term in the Hamiltonian correct, or should it be divided by two when written in this form? A quick check on some other websites suggest it is not correct. e.g. http://www.quantiki.org/wiki/Bose-Hubbard_model (plus others) Gierszep (talk) 20:03, 1 May 2011 (UTC)

A multiplicative constant would be there to count for effect of transfer between lattice sites on particle number, but it would be incorporated into the Hopping matrix element $t$. In this case, we're only counting each particle transfer once, so we do not need to divide by two, but on your quantiki page, the transfer is counted twice. Epic Wink (talk) 04:24, 4 December 2014 (UTC)

Messy

"Implementation in optical lattices" in particular could be cleaned up Epic Wink (talk) 04:24, 4 December 2014 (UTC)