A simple derivation of mean field limits for quantum systems

Abstract

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 the strategy yields with lesser effort 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.

References in corpus (3)

• Mean-Field Dynamics: Singular Potentials and Rate of Convergence
• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics

Cited by in corpus (4)

• Mean-Field Dynamics: Singular Potentials and Rate of Convergence
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• Dynamics of Large Boson Systems with Attractive Interaction and a Derivation of the Cubic Focusing NLS in ${\mathbb{R}}^3$
• Effective evolution equations from many body quantum dynamics