Scaling limits in the 3-D Schrödinger-Poisson system

DOI10.1016/S0893-9659(97)00084-0zbMath0888.35092OpenAlexW2046485970MaRDI QIDQ1376785

Juan Soler, José Luis López

Publication date: 17 February 1998

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(97)00084-0

zbMATH Keywords

rescalinglarge-time behaviour for the Schrödinger-Poisson problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40)

Related Items (4)

ASYMPTOTIC BEHAVIOR TO THE 3-D SCHRÖDINGER/HARTREE–POISSON AND WIGNER–POISSON SYSTEMS ⋮ TIME-DEPENDENT RESCALINGS AND LYAPUNOV FUNCTIONALS FOR THE VLASOV–POISSON AND EULER–POISSON SYSTEMS, AND FOR RELATED MODELS OF KINETIC EQUATIONS, FLUID DYNAMICS AND QUANTUM PHYSICS ⋮ A Space-Time Wigner Function Approach to Long Time Schrödinger--Poisson Dynamics ⋮ Asymptotic behaviour for the 3-D Schrödinger-Poisson system in the attractive case with positive energy

Cites Work

• Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
• On Wigner measures
• Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system
• On the equivalence of the Schrödinger and the quantum Liouville equations
• The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
• The One-Dimensional Wigner–Poisson Problem and Its Relation to the Schrödinger–Poisson Problem
• The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case
• Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner–Poisson and Schrödinger‐Poisson systems

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