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Quantum Phase diagram and time-of-flight absorption pictures of ultracold Bose system in a square optical superlattice
In this letter, by the use of the generalized effective potential theory,
with the help of process-chain approach under the framework of Kato formulation
of perturbation expansion, we calculate out the quantum phase diagram up to
8-th order for an ultracold Bose system in a square optical superlattice. Base
on these perturbative data, with the help of the linear fit extrapolation
technique, more accurate results are gotten, which are in excellent agreement
with recent Monte-Carlo numerical results. Moreover, by employing the
generalized re-summed Green's function method and cumulant expansion, the
momentum distribution function of the system is also calculated analytically
and the time-of-flight absorption pictures of the system are plotted.Comment: 6 pages, 6 figure
On the fast Khintchine spectrum in continued fractions
For , let be its continued fraction
expansion with partial quotients . Let be a function with as . In this note, the fast Khintchine spectrum, i.e., the Hausdorff
dimension of the set E(\psi):=\Big{x\in [0,1):
\lim_{n\to\infty}\frac{1}{\psi(n)}\sum_{j=1}^n\log a_j(x)=1\Big} is
completely determined without any extra condition on .Comment: 10 page
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