Empirical Measures and Quantum Mechanics: Applications to the Mean-Field Limit

In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of N -particle systems. We establish an equation governing the evolution of our quantum analogue of the N -particle empirical measure, and we prove that this equation contains the Hartree equati...

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Veröffentlicht in:	Communications in mathematical physics 2019-08, Vol.369 (3), p.1021-1053
Hauptverfasser:	Golse, François, Paul, Thierry
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Quantum Gravitation Classical mechanics Complex Systems Empirical equations Fourier transforms Mathematical and Computational Physics Mathematical Physics Particle density (concentration) Physics Physics and Astronomy Quantum mechanics Quantum Physics Relativity Theory Schrodinger equation Theoretical
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