Lars Onsager Prize (2021): Bose-Einstein condensate – a classical limit of matter waves

In 1925 A. Einstein predicted that at low temperature macroscopically large number of atoms of an ideal Bose gas are condensed in the lowest quantum state, creating Bose-Einstein condensate (BEC). Wave function of this state is a constant for a uniform stationary gas. However for an inhomogeneous gas in non-stationary condition this function depends on coordinates and time and satisfied the non-linear Gross-Pitaevskii equation (GPE). This equation demonstrates the wave nature of the condensates and plays a role in the theory of BEC which is analogous to a role of the Maxwell equations in the theory of the electromagnetism. Initially it was suggested by E.P. Gross and L.P. Pitaevskii in 1961 for description of a quantized vortex line, which existence in rotating BEC was predicted by L. Onsager in 1949. After BEC was achieved in 1995 by Cornell, Wieman and Ketterle, GEP was used for description of numerous observed phenomena. It was used for calculation of interference between two condensates, including in the presence of a vortex line, for calculation of structure and motion of solitons and vortex rings. New possibilities arise after realization of mixtures of BEC, which is described by a system of GPE. After creation of BEC of atoms with electrical or magnetic momenta the equation was generalized for these systems.