A Simple Derivation of Mean Field Limits for Quantum Systems

By P. Pickl. 2009

185 citations recorded by the source corpus.

We shall present a new strategy for handling mean field limits of quantum mechanical systems. The new method is simple and effective. It is simple, because it translates the idea behind the mean-field description of a many particle quantum system directly into a mathematical algorithm. It is effective because, with less effort, the strategy yields better results than previously achieved. As an instructional example we treat a simple model for the time-dependent Hartree equation which we derive under more general conditions than what has been considered so far. Other mean-field scalings leading, e.g. to the Gross-Pitaevskii equation can also be treated (Pickl in Derivation of the time dependent Gross Pitaevskii equation with external fields, preprint; Pickl in Derivation of the time dependent Gross Pitaevskii equation without positivity condition on the interaction, preprint).

Subfields: Acoustics and Ultrasonics, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a5d4975ed6434011355d67d188d49aec56cc105b

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In Acoustics and Ultrasonics

François Golse

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Citations in the corpus

Mean–Field Evolution of Fermionic Systems (2013, background): “In [32, 35], a different approach to obtain control of the rate of the convergence towards the Hartree evolution was proposed; its main advantage”
On the Dynamics of Large Particle Systems in the Mean Field Limit (2013, methodology): “The interested reader is referred to the original paper [80] for more details.”
On the Mean Field and Classical Limits of Quantum Mechanics (2015, background): “Moreover, quantitative estimates for that limit for ǫ fixed and N → ∞ have been obtained in [28, 26, 2].”
Derivation of Hartree's theory for generic mean-field Bose systems (2013, background): “There are many works on the related (but still different) derivation of the time-dependent Hartree theory from the time-dependent Schrödinger equation associated with the Hamiltonian HN , see for instance [29, 25, 63, 7, 20, 21, 3, 22, 24, 54, 34, 51].”