A simple proof of convergence to the Hartree dynamics in Sobolev trace norms

DOI10.1063/1.4968820zbMath1353.81132arXiv1608.01192OpenAlexW2477648203MaRDI QIDQ2951749

Michael Hott, Ioannis Anapolitanos

Publication date: 9 January 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.01192

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Geometry and structure of normed linear spaces (46B20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Quantum state spaces, operational and probabilistic concepts (81P16)

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Cites Work

• Dynamical collapse of Boson stars
• Rate of convergence towards Hartree dynamics
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• Quantum fluctuations and rate of convergence towards mean field dynamics
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
• Rate of convergence towards semi-relativistic Hartree dynamics
• Mean-field quantum dynamics with magnetic fields
• Mean field dynamics of boson stars
• Derivation of the Hartree equation for compound Bose gases in the mean field limit

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