Quantum States Allowing Minimum Uncertainty Product of angular position and momentum

We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle $\phi$ and its canonical moment $L_{z}$. We illustrate our results with analytical examples

CCDM model from quantum particle creation: constraints on dark matter mass

In this work the results from the quantum process of matter creation have been used in order to constrain the mass of the dark matter particles in an accelerated Cold Dark Matter model (Creation Cold Dark Matter, CCDM). In order to take into account a back reaction effect due to the particle creation phenomenon, it has been assumed a small deviation $\varepsilon$ for the scale factor in the matter dominated era of the form $t^{\frac{2}{3}+\varepsilon}$. Based on recent $H(z)$ data, the best fit values for the mass of dark matter created particles and the $\varepsilon$ parameter have been found as $m=1.6\times10^3$ GeV, restricted to a 68.3\% c.l. interval of ($1.5<m<6.3\times10^7$) GeV and $\varepsilon = -0.250^{+0.15}_{-0.096}$ at 68.3\% c.l. For these best fit values the model correctly recovers a transition from decelerated to accelerated expansion and admits a positive creation rate near the present era. Contrary to recent works in CCDM models where the creation rate was phenomenologically derived, here we have used a quantum mechanical result for the creation rate of real massive scalar particles, given a self consistent justification for the physical process. This method also indicates a possible solution to the so called "dark degeneracy", where one can not distinguish if it is the quantum vacuum contribution or quantum particle creation which accelerates the Universe expansion.Comment: 16 pages, 5 figures. Major modifications have been done, following the referee suggestions. The deduction of the treatment is now more transparent, figures have been added showing the statistical limits over the dark matter mass, and the best fit for DM mass has been slightly modifie