Weak Copling Limit of the N-Particle Schrödinger Equation

By François Golse, Claude Bardos, Norbert J. Mauser. 2000

160 citations recorded by the source corpus.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/026fd8f3ecc39b67dce718231e49bcc37e656ef6

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In Mathematical Physics

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Citations in the corpus

Mean field dynamics of boson stars (2005, result): “Partial results for the non-relativistic Coulomb case were also established in [ 1 ].”
Derivation of the nonlinear Schr\"odinger equation from a many body Coulomb system (2001, background): “e-print archive: http://xxx.lanl.gov/math-ph/0111042 AMS 2000 Subject Classification: 35Q55, 45F15, 81Q05, 81V70 Keywords: Nonlinear Hartree equation, Mean field Coulomb system of bosons, BBGKY hierarchy”
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate (2004, unknown): “See the work of Hepp [10] and Spohn [26] for bounded potentials and [2, 5] for potentials with Coulomb type singularity.”
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems (2005, unknown): “Keywords: Feynman diagrams, BBGKY hierarchy, dispersive estimates, propagation of chaos.”
Kac’s program in kinetic theory (2011, methodology): “The BBGKY hierarchy method revisited The so-called BBGKY hierarchy method (Bogoliubov, Born, Green, Kirkwood and Yvon) is very popular in physics and mathematics for studying many-particle systems: see for instance [3] where this approach is used for Kac’s master equation for hard spheres, or see, a”
Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics (2007, background): “5) for a Coulomb interaction V (x) = const/|x| (partial results for the Coulomb interaction were also obtained by Bardos, Golse, and Mauser in [2]).”
Effective Evolution Equations from Quantum Dynamics (2015, methodology): “The BBGKY technique has been later extended to potentials with Coulomb singularity in [30, 9] and, for semi-relativistic bosons, in [26].”
Derivation of the Gross‐Pitaevskii hierarchy for the dynamics of Bose‐Einstein condensate (2004, unknown): “See the work of Hepp [11] and Spohn [27] for bounded potentials and [2, 6] for potentials with Coulomb type singularity.”
Mean field dynamics of fermions and the time-dependent Hartree-Fock equation (2002, unknown): “We follow the app of Spohn, who derived a mean field dynamical equation (the time-dependent H equation) for mean field systems of distinguishable particles, remarking at the tim “the convergence of the mean field limit with statistics included is an open problem” [1 see [2] for a complete proof of S”
On the Mean Field and Classical Limits of Quantum Mechanics (2015, methodology): “for fixed, has been proved by other methods in this case (see [4,29]).”
The mean-field limit for the dynamics of large particle systems (2003, background): “3 in [5], to which we refer for a proof).”