BZ Seminar in Analysis: Benjamin Schlein (Bonn)

Mean field and Gross-Pitaevskii limits of quantum dynamics

The derivation of effective evolution equations is a central question in non-equilibrium statistical mechanics. In the so called mean field limit, the many body quantum evolution can be approximated by the nonlinear Hartree equation. We will discuss how optimal estimates on the rate of the convergence and a central limit theorem for the fluctuations around the Hartree dynamics can be obtained making use of so called coherent states. The Gross-Pitaevskii regime is a very singular mean field limit, relevant for the description of the dynamics of Bose-Einstein condensates. In this case, we will show how the convergence towards the limiting dynamics can be established by a modification of the coherent states ansatz with appropriate Bogoliubov transformations, which describe the correlation structure developed by the many body evolution because of the singularity.

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