Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

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We consider the semi-relativistic system of N gravitating Bosons with gravitation constant G. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where N -> a and G -> 0 while GN = lambda fixed. In the super-critical regime of large lambda, we introduce the regularized interaction where the cutoff vanishes as N -> a. We show that the difference between the many-body semi-relativistic Schrodinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order N (-1) for all lambda, i.e., the result covers the sub-critical regime and the super-critical regime. The N dependence of the bound is optimal.
Publisher
SPRINGER BASEL AG
Issue Date
2013-03
Language
English
Article Type
Article
Keywords

GROSS-PITAEVSKII EQUATION; CLASSICAL FIELD LIMIT; MANY-BOSON SYSTEMS; QUANTUM-MECHANICS; SCATTERING THEORY; DERIVATION; COLLAPSE; STARS

Citation

ANNALES HENRI POINCARE, v.14, no.2, pp.313 - 346

ISSN
1424-0637
DOI
10.1007/s00023-012-0188-6
URI
http://hdl.handle.net/10203/174519
Appears in Collection
MA-Journal Papers(저널논문)
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