Abstract
Nonlinear effects lie amongst the most interesting phenomena in physical, chemical and biological systems. In quantum physics nonlinearity is provided by inter-particle interactions. A theoretical many-body description can be made in the framework of the mean field approximation, which yields the Hartree-Fock equations for a system of interacting fermions and the Gross-Pitaevskii equation for interacting bosons. The latter is widely applied to Bose-Einstein condensates (BECs) of cold atoms and satisfactorily describes a variety of nonlinear phenomena, such as the superfluid transition, formation of single vortices and vortex lattices. From the mathematical point of view the Gross-Pitaevskii equation is equivalent to the nonlinear Schrödinger equation, used in nonlinear optics for the description of self-focusing and soliton propagation.
© 2012 Optical Society of America
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