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Gravity, Bose-Einstein Condensates and Gross-Pitaevskii Equation
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small-amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈1020, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a 1/r3 gravity at short scales.
Keywords
Bose–Einstein Condensate, Gross–Pitaevskii Equation, Instability, Large Extra Dimension Gravity.
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