Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics

Mean-Field Dynamics: Singular Potentials and Rate of Convergence

We consider the time evolution of a system of N identical bosons whose interaction potential is rescaled by N. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the meanfield limit N → ∞ the quantum N -body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we exte...

On Mean Field Convergence and Stationary Regime

Assume that a family of stochastic processes on some Polish space E converges to a deterministic process; the convergence is in distribution (hence in probability) at every fixed point in time. This assumption holds for a large family of processes, among which many mean field interaction models and is weaker than previously assumed. We show that any limit point of an invariant probability of th...

Quantum Dynamics with Mean Field Interactions: a New Approach

We propose a new approach for the study of the time evolution of a factorized N -particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one...

Quantum fluctuations, decoherence of the mean field, and structure formation in the early Universe.

Differences between mean-field dynamics and N-particle quantum dynamics as a signature of entanglement.

A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introduc...