Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems dedicated to Helmut Neunzert at the occasion of his 60th birthday

I. Gasser; R. Illner; P. A. Markowich; C. Schmeiser

doi:10.1051/m2an/1998320606991

Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems dedicated to Helmut Neunzert at the occasion of his 60th birthday

I. Gasser^*, R. Illner, P. A. Markowich, C. Schmeiser

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We analyze the semiclassical limit and the "t → ∞ asymptotics" of mildly nonlinear Schrödinger systems of (self-consistent) Hartree-Fock form. Using Wigner-funclion techniques we prove that the semiclassical limit is represented by the self-consistent Vlasov equation. Moreover we prove time decay for the position density and for the Hartree-potential in L^p norms as t → ∞.

Original language	English (US)
Pages (from-to)	699-713
Number of pages	15
Journal	Mathematical Modelling and Numerical Analysis
Volume	32
Issue number	6
DOIs	https://doi.org/10.1051/m2an/1998320606991
State	Published - 1998
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Analysis
Applied Mathematics
Numerical Analysis
Modeling and Simulation

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abstract = "We analyze the semiclassical limit and the {"}t → ∞ asymptotics{"} of mildly nonlinear Schr{\"o}dinger systems of (self-consistent) Hartree-Fock form. Using Wigner-funclion techniques we prove that the semiclassical limit is represented by the self-consistent Vlasov equation. Moreover we prove time decay for the position density and for the Hartree-potential in Lp norms as t → ∞.",

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T1 - Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems dedicated to Helmut Neunzert at the occasion of his 60th birthday

AU - Gasser, I.

AU - Illner, R.

AU - Markowich, P. A.

AU - Schmeiser, C.

PY - 1998

Y1 - 1998

N2 - We analyze the semiclassical limit and the "t → ∞ asymptotics" of mildly nonlinear Schrödinger systems of (self-consistent) Hartree-Fock form. Using Wigner-funclion techniques we prove that the semiclassical limit is represented by the self-consistent Vlasov equation. Moreover we prove time decay for the position density and for the Hartree-potential in Lp norms as t → ∞.

AB - We analyze the semiclassical limit and the "t → ∞ asymptotics" of mildly nonlinear Schrödinger systems of (self-consistent) Hartree-Fock form. Using Wigner-funclion techniques we prove that the semiclassical limit is represented by the self-consistent Vlasov equation. Moreover we prove time decay for the position density and for the Hartree-potential in Lp norms as t → ∞.

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U2 - 10.1051/m2an/1998320606991

DO - 10.1051/m2an/1998320606991

M3 - Article

AN - SCOPUS:0039982895

SN - 0764-583X

VL - 32

SP - 699

EP - 713

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 6

ER -

Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems dedicated to Helmut Neunzert at the occasion of his 60th birthday

Abstract

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