Mean-field quantum dynamics with magnetic fields

Abstract

We consider a system of $N$ bosons in three dimensions interacting through a mean-field Coulomb potential in an external magnetic field. For initially factorized states we show that the one-particle density matrix associated with the solution of the $N$-body Schrödinger equation converges to the projection onto the solution of the magnetic Hartree equation in trace norm and in energy as $N\to \infty$. Estimates on the rate of convergence are provided.

21 pages, typos corrected, to appear in J. Math. Phys

References in corpus (4)

• Mean-Field Dynamics: Singular Potentials and Rate of Convergence
• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• Rate of Convergence Towards Hartree Dynamics
• Dynamical Collapse of Boson Stars

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• Derivation of the Hartree equation for compound Bose gases in the mean field limit
• Randomization and the Gross-Pitaevskii hierarchy
• A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
• Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
• Mean-field limits of particles in interaction with quantized radiation fields
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms