Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems

Details Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems

2005-08-02

arxiv.org/abs/math-ph/0508010v3

Physics

Mathematical Physics

72 pages, 17 figures. Final version

Scientific paper

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 $k$.

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