Semi-classical limit of Schrodinger-Poisson equations in space dimension at least 3

Abstract

We prove the existence of solutions to the Schrodinger-Poisson system on a time interval independent of the Planck constant, when the doping profile does not necessarily decrease at infinity, in the presence of a subquadratic external potential. The lack of integrability of the doping profile is resolved by working in Zhidkov spaces, in space dimension at least three. We infer that the main quadratic quantities (position density and modified momentum density) converge strongly as the Planck constant goes to zero. When the doping profile is integrable, we prove pointwise convergence.

30 pages. To appear in JDE

References in corpus (3)

• Geometric optics and instability for semi-classical Schrodinger equations
• WKB analysis for nonlinear Schrödinger equations with potential
• Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

Cited by in corpus (4)

• On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit
• WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
• An asymptotic preserving approach for nonlinear Schrodinger equation in the semiclassical limit
• High-frequency averaging in semi-classical Hartree-type equations