Mathematics – Analysis of PDEs
Scientific paper
2008-03-15
Mathematics
Analysis of PDEs
25 pages, 2 figures
Scientific paper
We study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We derive apriori dispersive estimates that express the overall repulsive nature of the particle interactions. These estimates hold for a wide class of two-body interaction potentials which are independent of the particle number, N. We discuss applications of these estimates to the BBGKY hierarchy for reduced density matrices analyzed by Elgart, Erdos, Schlein and Yau.
Grillakis Manoussos G.
Margetis Dionisios
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