- 05-280 Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
- Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
Aug 19, 05
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Abstract. We prove rigorously that the one-particle density matrix of
interacting Bose systems with a short-scale repulsive pair
interaction converges to the solution of the cubic non-linear
Schr\"odinger equation in a suitable scaling limit.
The result is extended to
$k$-particle density matrices for all positive integer $k$.