 Gross–Pitaevskii equation

The Gross–Pitaevskii equation describes a dilute interacting condensate through a complex order parameter $\psi$, normalized so that $|\psi {|}^2$ is number density. Repulsive contact interactions have $g>0$. In a frame rotating at the condensate frequency, the operator includes $-\mu$, with chemical potential $\mu$. It is generated by a Hamiltonian functional; its homogeneous positive-density state has $n_0=\mu /g$ when $g,\mu >0$.

The Gross–Pitaevskii equation (GPE) is a nonlinear partial differential equation that describes the evolution of a complex wave function associated with a Bose-Einstein condensate (BEC), a state of matter formed at very low temperatures where a group of bosons occupy the same quantum state. The equation is named after physicists Eugene Pitaevskii and Lev Gross, who contributed to its formulation.