Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
(1240K, Postscript)
ABSTRACT. We prove rigorously that the one-particle density matrix of
three dimensional
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 $k$.