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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...
A derivation of the Breit equation from Barut's covariant formulation of electrodynamics in terms of direct interactions
Breit equation Barut's covariant formulation Quantum Physics High Energy Physics - Theory
2011/10/10
Abstract: We study Barut's covariant equations describing the electromagnetic interactions between N spin-1/2 particles. In the covariant formulation each particle is described by a Dirac spinor. It i...
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...
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field
Processes in random environments Quantum field theory Coherent states Kinetic theory of gases
2011/8/25
Abstract: The linear Boltzmann equation is derived from a microscopic quantum model of a particle interacting, in the weak coupling limit, with a translation invariant and centered Gaussian random fie...