THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY

DOI10.1142/S021989160800160XzbMath1165.35048MaRDI QIDQ5506455

Xiaomei Liao, Xu Yang, Shih Jin

Publication date: 28 January 2009

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Fokker-Planck equationsemiclassical limitVlasov-Poisson systemmulti-valued solutionSchrödinger -Poisson equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Generalized solutions to partial differential equations (35D99)

Related Items (2)

A high order numerical method for computing physical observables in the semiclassical limit of the one-dimensional linear Schrödinger equation with discontinuous potentials ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Cites Work

• Discretization of Dirac delta functions in level set methods
• Concentrations in the one-dimensional Vlasov-Poisson equations. I: Temporal development and non-unique weak solutions in the single component case
• Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. III: From ab initio models to WKB for Schrödinger-Poisson
• Particle Methods for the One-Dimensional Vlasov–Poisson Equations
• Homogenization limits and Wigner transforms
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• Numerical Approximations of Pressureless and Isothermal Gas Dynamics
• THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D
• TWO MOMENT SYSTEMS FOR COMPUTING MULTIPHASE SEMICLASSICAL LIMITS OF THE SCHRÖDINGER EQUATION

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