A Klein-Gordon model with cubic and logarithmic interactions supports self-trapped quantum droplet solutions whose non-relativistic limit yields a generalized Gross-Pitaevskii equation with logarithmic correction.
Relativistic bose–einstein condensates: a new system for analogue models of gravity.New Journal of Physics, 12(9):095012
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Emergent Quantum Droplets in Logarithmic Klein-Gordon Models of Bose-Einstein Condensates
A Klein-Gordon model with cubic and logarithmic interactions supports self-trapped quantum droplet solutions whose non-relativistic limit yields a generalized Gross-Pitaevskii equation with logarithmic correction.