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Derivation of the Grossā€Pitaevskii hierarchy for the dynamics of Boseā€Einstein condensate

Derivation of the Grossā€Pitaevskii hierarchy for the dynamics of Boseā€Einstein condensate

Abstract Consider a system of N bosons on the threeā€dimensional unit torus interacting via a pair potential N 2 V ( N ( x i āˆ’ x j )) where x = ( x 1 , ā€¦, x N ) denotes the positions of the particles. Suppose that the initial ā€¦