Mean field limit of bosonic systems in partially factorized states and their linear combinations

Abstract

We study the mean field limit of one-particle 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 time-evolved 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 Hilbert-Schmidt norm towards a mixed state, combination of projections on different solutions (corresponding to each initial datum), for states that are a linear superposition.

17 pages

References in corpus (3)

• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Classical limit of the Nelson model with cut off
• Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data

Cited by in corpus (2)

• On the rate of convergence for the mean field approximation of many-body quantum dynamics
• Mean field approximation of many-body quantum dynamics for Bosons in a discrete numerical model