From Schrödinger dynamics to the Euler equations

Bruno Nachtergaele University of California, Davis

We show that, in the hydrodynamic limit, the Heisenberg dynamics of the energy, momentum, and particle densities for fermions with short-range pair interactions converges to the compressible Euler equations with the pressure function given by quantum statistical mechanics. Our derivation is based on a quantum version of the entropy method and a suitable quantum virial theorem. We require a number of technical conditions that will be discussed in the talk.