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We study the occupation numbers and number fluctuations of ultra-cold atomsin deep optical lattices for finite temperatures within the Bose-Hubbard model.Simple analytical expressions for the mean occupation number and numberfluctuations are obtained in the weak-hopping regime using an interpolationbetween results from different perturbation approaches in the Mott-insulatorand superfluid phases. These analytical results are compared to exact onedimensional numerical calculations using a finite temperature variant of theDensity-Matrix Renormalisation Group (DMRG) method and found to have a highdegree of accuracy. We also find very good agreement in the crossover``thermal'' region. With the present approach the magnitude of numberfluctuations under realistic experimental conditions can be estimated and theproperties of the finite temperature phase diagram can be studied.Comment: 4 pages, 1 eps figure, submitted to PR

Occupation number and fluctuations in the finite-temperature Bose-Hubbard model