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A. Jüngel:
"Lagrangian structure of quantum fluid models in the space of probability measures";
Keynote Lecture: Workshop on Dissipative Evolutions and Convergence to Equilibrium, Toulouse (invited); 2011-09-27 - 2011-09-30.

It is well known that the Schroedinger equation in the
Madelung representation can be derived from the Euler-Lagrange
equation with a Lagrangian involving the kinetic and potential
energies and the Fisher information. We extend previous works due
to Nelson, Lafferty, and von Renesse by deriving novel quantum
fluid models using the optimal transport calculus. The advantage
of the Lagrangian approach is its flexibility and geometric
interpretation.
More precisely, we derive first Madelung-type equations for
charged particles in a magnetic field and explore their symplectic
structure. Then, from a dissipative Euler-Lagrange equation, quantum
Navier-Stokes equations are obtained. This model allows for two
different energy-dissipation equations whose existence can be
explained by a variant of the Noether theorem.

Siehe englisches Abstract.

Lagrangian mechanics; quantum fluids; quantum Navier-Stokes model