Applied Analysis Reading Group

26 March 2012: Max von Renesse

Hamiltonian Mechanics on Wasserstein Space and Quantum Fluid Models

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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