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Witness that the invariance of each invariant separately follows immediately from the $\propto \,S^2$ scaling of the area of the entrance / exit window with the distance $S$. The invariance of each is really a restatement of this scaling law. So it now remains to prove the equality of the two potentially different invariants i.e. the one calculated for the ...

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The curvature of the drop is influenced by the liquid-solid, solid-air and liquid-air interface forces. It can be determined by the Young-Laplace equation. For more details see this article

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A good reference for choosing appropriate laser beam for a given type of atom, plz read Michal J Martin's PhD thesis at jila, Prof. Ye Jun's group site. Some moderator would not be happy with links so I delete it. Chapter 2 & 4 all provides condensed materials about laser wavelength.

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As you know that the speckles in the laser comes from the low bandwidth of the laser. Hence to reduce the speckles one need to increase the bandwidth of the laser or to reduce the coherence properties of the laser. Similar to the reference given by you same authors also published another findings in nature photonics. The best solution would be to use a ...

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