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- W2952205957 abstract "Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $bx=(x_1, >..., x_N)$ denotes the positions of the particles. Let $H_N$ denote the Hamiltonian of the system and let $psi_{N,t}$ be the solution to the Schrodinger equation. Suppose that the initial data $psi_{N,0}$ satisfies the energy condition [ leq C^k N^k ] for $k=1,2,... $. We also assume that the $k$-particle density matrices of the initial state are asymptotically factorized as $Ntoinfty$. We prove that the $k$-particle density matrices of $psi_{N,t}$ are also asymptotically factorized and the one particle orbital wave function solves the Gross-Pitaevskii equation, a cubic non-linear Schrodinger equation with the coupling constant given by the scattering length of the potential $V$. We also prove the same conclusion if the energy condition holds only for $k=1$ but the factorization of $psi_{N,0}$ is assumed in a stronger sense." @default.
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- W2952205957 date "2006-06-05" @default.
- W2952205957 modified "2023-10-18" @default.
- W2952205957 title "Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate" @default.
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