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Jul
2
awarded  Curious
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
Adam, yes I agree with you. My question is not from your comments. It is from Greiner's thesis about TF approximation:-) It says "In a Thomas Fermi approximation we can neglect the contribution of the kinetic energy term ".
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
so that means TF only works for weakly interacting regime $t/U \gg1$. Then my question is why TF approximation ignores the kinetic energy term as stated in M. Greiner's PhD thesis greiner.physics.harvard.edu/PDF%20Files/PhD_greiner.pdf. Page 34-36.
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
I tried to use TF approximation, but the result is very unreasonable. For example,in 2D system, $t/U=0.1$, $\mu/U=0.6$,$\Omega/U=0.036$, using TF approximation, I can get the total particle number$N_{tot} =\int_0^{2\pi}d\phi\int_0^{R_{TF}} (\mu-\Omega r^2)r dr $. Plugging $R_{FT}=\sqrt{\frac{\mu}{\Omega}}$ in it, one can get $N_{tot} =2\pi(\frac{\mu R_{TF}^2}{2}-\frac{\Omega R_{TF}^4}{4})=\frac{\pi \mu^2}{2\Omega}\simeq 16$. However, the exact total particle number is 67 by Gutzwiller method.
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
I totally agree with all your points above. My question is: is there any quick method to roughly get the total density in a trap when given $t$,$U$,$\mu$ and trapping potential $\Omega$. For a 2D system in strong interacting regime with a Mott plateau of unitary filling in the trap center, one can get the roughly density $N_{tot}\simeq \pi*R_{Mott}^2=\pi*\frac{\mu}{\Omega}.$ But how to quickly get an approximation total particle number for weakly interacting regime without performing numeric calculation?
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
Now I am confused.Thomas-Fermi approximation is valid for Gross-Pitaevski regime in which the hopping is dominant, but why the Thomas-Fermi ignores the kinetic energy term? In Bose-Hubbard model, only given micro-parameters hopping t,interaction U and chemical potential $\mu$, one can calculate the total particle number,right?
Jun
4
awarded  Editor
Jun
4
comment Thomas-Fermin approximation of cold atoms in a harmonic trap
Yes, you are right. Thanks.
Jun
4
revised Thomas-Fermin approximation of cold atoms in a harmonic trap
added 4 characters in body
Jun
3
asked Thomas-Fermin approximation of cold atoms in a harmonic trap
May
29
accepted Why the trap is needed in cold atom experiment?
May
29
asked Why the trap is needed in cold atom experiment?
May
27
asked How to load Bose-Einstein Condensates into an optical lattice?
May
25
awarded  Tumbleweed
May
18
asked Phase coherence and interference effects in Anderson localization
May
15
comment Gutzwiller mean-field method in Bose Hubbard model
@Adam Yes, I agree with you. Assume the total sites is M and maximum occupation number on each site is N_c. My confusion is why the Gutzwiller wavefunciton amplitudes (calculate the N_c+1 vector f on each site, then glue f's of each site together, so it becomes a M*(N_c+1) vector)calculated by LDA is different from the wavefunciton amplitudes f's calculated by minimizing the M*(N_c+1) parameters directly.
May
14
comment Gutzwiller mean-field method in Bose Hubbard model
@Adam Thanks! By LDA I mean treat each site independently with a local potential and solve it with Gutzwiller method. I know in most cases, people use LDA as an initial guess to minimize the energy and find the ground sate.
May
14
asked Gutzwiller mean-field method in Bose Hubbard model
May
6
awarded  Scholar
May
6
accepted Similarity between spinless fermion and weakly interacting bosons