Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
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 Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.
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