Generalization of the Gross–Pitaevskii equation for multi-particle cases
Nicolai BogoliubovSteklov Institute of Mathematics of the Russian Academy of Sciences, Moscow 119991, RussiaM. Yu. RasulovaInstitute of Nuclear Physics Academy of Sciences of Uzbekistan, Tashkent 100214, UzbekistanTohir Vohidovich AkramovNational University of Uzbekistan named after M. Ulugbek, Institute of Nuclear Physics Academy of Sciences of Uzbekistan, Tashkent 100214, Uzbekistan
ABI
Abstract
A new method is proposed to obtain Gross–Pitaevskii equation by the chain of Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) quantum kinetic equations. In that sense, we investigate the dynamics of a quantum system including infinite number of identical particles which interact via a (special) pair potential on the form of Dirac delta-function.
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