Otto's Riemannian Framework for the Wasserstein space of probablity measures allows not only for first order gradient flows but also for second order Hamiltonian ODEs. As a result we give a concise representation of the Schrödinger equation for wave functions as an instance of Newton's classical law of motion on Wasserstein space, the two representations being related by a natural sympelctic morphism. Introducting friction leads to dissipative quantum fluid models such as the Quantum Navier Stokes equation, which was derived as a model for a tagged particle in a many body quantum system.
Partially based on joint works with A. Jüngel and P. Fuchs (Vienna)
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