, Volume 288, Issue 3, pp 1023-1059
Date: 28 Feb 2009

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

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In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg- picture dynamics of “observables”, thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a “semi-classical” limit.

Communicated by H.-T. Yau