An equation describing these systems has a one-dimensional soliton solution with value proportional to the hyperbolic tangent of "one over radical two times displacement over healing length".
When these systems incorporate only repulsive interactions, their phonon spectra do not exhibit an energy gap by the Hugenholtz-Pines theorem. An equation describing these systems has a one-dimensional soliton solution with value proportional to the hyperbolic tangent of "one over radical two times displacement over healing length". That equation describing these systems includes a coupling constant equal to "four pi times h-bar squared times scattering length over  mass" and introduces a  (*)  nonlinear pseudopotential term into  the SchrÃ¶dinger equation under the Hartree-Fock approximation. In the dilute regime, the single particle wavefunction for one of these systems is given by the Gross-Pitaevskii equation. For 10 points, name this exotic form of matter consisting of supercooled atoms with integer spin that occupy the same quantum state.
When these systems incorporate only repulsive interactions, their phonon spectra do not exhibit an energy gap by the Hugenholtz-Pines theorem.
Bose-Einstein condensates [or  BECs; prompt on "Bose gases" or anything mentioning "bosons"]