Mean field limit of bosonic systems in partially factorized states and their linear combinations
Abstract
We study the mean field limit of oneparticle reduced density matrices, for a bosonic system in an initial state with a fixed number of particles, only a fraction of which occupies the same state, and for linear combinations of such states. In the mean field limit, the timeevolved reduced density matrix is proved to converge: in trace norm, towards a rank one projection (on the state solution of Hartree equation) for a single state; in HilbertSchmidt norm towards a mixed state, combination of projections on different solutions (corresponding to each initial datum), for states that are a linear superposition.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.5699
 Bibcode:
 2013arXiv1305.5699F
 Keywords:

 Mathematical Physics
 EPrint:
 17 pages