Talk:Bose–Hubbard model

message: 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)
thread_title:  Links 

message: 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)
replies: text: An acoustic black hole is simply a region of space where sound waves fall in, and can't get out. This can happen for a large variety of reasons; one fun lab example is a waterfall, where the water falls faster than the speed of surface waves, and so surface-waves (ripples) cannot get "back up" the waterfall. This is a perfectly reasonable topic to explore, and did not require removal. 67.198.37.16 (talk) 17:30, 15 May 2024 (UTC)
thread_title:  Black Holes 

message: 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)
thread_title: correct Hamiltonian?

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