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On the Rigorous Derivation of the 3D Cubic Nonlinear Schr鰀inger Equation with A Switchable Quadratic Trap
Gross-Pitaevskii Hierarchy Switchable Quadratic Trap Collapsing Estimate Klainerman-Machedon Board Game and Space-time Bound
2012/4/17
We consider the dynamics of the 3D N-body Schr\"odinger equation in the presence of a switchable quadratic trap. We assume the pair interaction potential is N^{3{\beta}-1}V(N^{{\beta}}x). We justify t...
On Rigorous Derivation of the Enskog Kinetic Equation
BBGKY hierarchy Enskog equation kinetic cluster expansion scattering cumulant hard spheres
2011/9/22
Abstract: We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operato...