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

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

2008-05-28

arxiv.org/abs/0805.4299v2

Physics

Mathematical Physics

Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1)

Scientific paper

10.1007/s00220-009-0754-z

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.

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